diff --git a/src/storage/dd/Add.cpp b/src/storage/dd/Add.cpp
index a8fc25f56..67297f627 100644
--- a/src/storage/dd/Add.cpp
+++ b/src/storage/dd/Add.cpp
@@ -595,12 +595,12 @@ namespace storm {
         
         template<DdType LibraryType, typename ValueType>
         AddIterator<LibraryType, ValueType> Add<LibraryType, ValueType>::begin(bool enumerateDontCareMetaVariables) const {
-            return internalAdd.begin(this->getContainedMetaVariables(), enumerateDontCareMetaVariables);
+            return internalAdd.begin(this->getDdManager(), this->getContainedMetaVariables(), enumerateDontCareMetaVariables);
         }
         
         template<DdType LibraryType, typename ValueType>
         AddIterator<LibraryType, ValueType> Add<LibraryType, ValueType>::end(bool enumerateDontCareMetaVariables) const {
-            return internalAdd.end(enumerateDontCareMetaVariables);
+            return internalAdd.end(this->getDdManager(), enumerateDontCareMetaVariables);
         }
         
         template<DdType LibraryType, typename ValueType>
@@ -630,6 +630,11 @@ namespace storm {
             return Bdd<DdType::CUDD>(this->getDdManager(), internalAdd.toBdd(), this->getContainedMetaVariables());
         }
 
+        template<DdType LibraryType, typename ValueType>
+        Add<LibraryType, ValueType>::operator InternalAdd<LibraryType, ValueType>() const {
+            return internalAdd;
+        }
+        
         template class Add<storm::dd::DdType::CUDD, double>;
     }
 }
\ No newline at end of file
diff --git a/src/storage/dd/Add.h b/src/storage/dd/Add.h
index c42a0fb4c..1a67f5dce 100644
--- a/src/storage/dd/Add.h
+++ b/src/storage/dd/Add.h
@@ -25,6 +25,7 @@ namespace storm {
         public:
             friend class DdManager<LibraryType>;
             friend class Bdd<LibraryType>;
+            friend class Odd<LibraryType>;
             
             // Instantiate all copy/move constructors/assignments with the default implementation.
             Add() = default;
@@ -629,8 +630,7 @@ namespace storm {
             /*!
              * We provide a conversion operator from the BDD to its internal type to ease calling the internal functions.
              */
-            operator InternalAdd<LibraryType, ValueType>();
-            operator InternalAdd<LibraryType, ValueType> const() const;
+            operator InternalAdd<LibraryType, ValueType>() const;
             
             /*!
              * Converts the ADD to a row-grouped (sparse) double matrix. If the optional vector is given, it is also
diff --git a/src/storage/dd/AddIterator.h b/src/storage/dd/AddIterator.h
index 17186a874..ebcb40910 100644
--- a/src/storage/dd/AddIterator.h
+++ b/src/storage/dd/AddIterator.h
@@ -7,7 +7,7 @@ namespace storm {
     namespace dd {
         // Declare DdIterator class so we can then specialize it for the different DD types.
         template<DdType Type, typename ValueType>
-        class DdForwardIterator;
+        class AddIterator;
     }
 }
 
diff --git a/src/storage/dd/Bdd.cpp b/src/storage/dd/Bdd.cpp
index 7f9f5830c..08c47a82f 100644
--- a/src/storage/dd/Bdd.cpp
+++ b/src/storage/dd/Bdd.cpp
@@ -37,7 +37,7 @@ namespace storm {
         template<DdType LibraryType>
         template<typename ValueType>
         Bdd<LibraryType> Bdd<LibraryType>::fromVector(std::shared_ptr<DdManager<LibraryType> const> ddManager, std::vector<ValueType> const& values, Odd<DdType::CUDD> const& odd, std::set<storm::expressions::Variable> const& metaVariables, std::function<bool (ValueType const&)> const& filter) {
-            return Bdd<LibraryType>(ddManager, InternalBdd<LibraryType>::fromVector(ddManager, values, odd, ddManager->getSortedVariableIndices(metaVariables), filter), metaVariables);
+            return Bdd<LibraryType>(ddManager, InternalBdd<LibraryType>::fromVector(&ddManager->internalDdManager, values, odd, ddManager->getSortedVariableIndices(metaVariables), filter), metaVariables);
         }
         
         template<DdType LibraryType>
@@ -176,7 +176,7 @@ namespace storm {
         
         template<DdType LibraryType>
         storm::storage::BitVector Bdd<LibraryType>::toVector(storm::dd::Odd<LibraryType> const& rowOdd) const {
-            return internalBdd.toVector(rowOdd);
+            return internalBdd.toVector(rowOdd, this->getDdManager()->getSortedVariableIndices());
         }
         
         template<DdType LibraryType>
@@ -233,12 +233,7 @@ namespace storm {
         }
         
         template<DdType LibraryType>
-        Bdd<LibraryType>::operator InternalBdd<LibraryType>() {
-            return internalBdd;
-        }
-
-        template<DdType LibraryType>
-        Bdd<LibraryType>::operator InternalBdd<LibraryType> const() const {
+        Bdd<LibraryType>::operator InternalBdd<LibraryType>() const {
             return internalBdd;
         }
         
diff --git a/src/storage/dd/Bdd.h b/src/storage/dd/Bdd.h
index 17671f2ed..5f672453d 100644
--- a/src/storage/dd/Bdd.h
+++ b/src/storage/dd/Bdd.h
@@ -241,8 +241,7 @@ namespace storm {
             /*!
              * We provide a conversion operator from the BDD to its internal type to ease calling the internal functions.
              */
-            operator InternalBdd<LibraryType>();
-            operator InternalBdd<LibraryType> const() const;
+            operator InternalBdd<LibraryType>() const;
             
             /*!
              * Creates a DD that encapsulates the given CUDD ADD.
diff --git a/src/storage/dd/Dd.h b/src/storage/dd/Dd.h
index be3181f3c..e347f1021 100644
--- a/src/storage/dd/Dd.h
+++ b/src/storage/dd/Dd.h
@@ -11,14 +11,21 @@
 namespace storm {
     namespace dd {
         // Forward-declare some classes.
-        template<DdType LibraryType> class DdManager;
-        template<DdType LibraryType> class Bdd;
+        template<DdType LibraryType>
+        class DdManager;
+        
+        template<DdType LibraryType>
+        class Bdd;
+
+        template<DdType LibraryType>
+        class Odd;
         
         template<DdType LibraryType>
         class Dd {
         public:
             // Declare the DdManager so it can access the internals of a DD.
             friend class DdManager<LibraryType>;
+            friend class Odd<LibraryType>;
             
             // Instantiate all copy/move constructors/assignments with the default implementation.
             Dd() = default;
diff --git a/src/storage/dd/DdManager.cpp b/src/storage/dd/DdManager.cpp
index 28b57a866..95226f8aa 100644
--- a/src/storage/dd/DdManager.cpp
+++ b/src/storage/dd/DdManager.cpp
@@ -118,8 +118,8 @@ namespace storm {
                 variables.emplace_back(Bdd<DdType::CUDD>(this->shared_from_this(), ddVariablePair.second, {unprimed}));
             }
 
-            metaVariableMap.emplace(unprimed, DdMetaVariable<LibraryType>(name, low, high, variables, this->shared_from_this()));
-            metaVariableMap.emplace(primed, DdMetaVariable<LibraryType>(name + "'", low, high, variablesPrime, this->shared_from_this()));
+            metaVariableMap.emplace(unprimed, DdMetaVariable<LibraryType>(name, low, high, variables));
+            metaVariableMap.emplace(primed, DdMetaVariable<LibraryType>(name + "'", low, high, variablesPrime));
             
             return std::make_pair(unprimed, primed);
         }
@@ -141,8 +141,8 @@ namespace storm {
             variables.emplace_back(Bdd<DdType::CUDD>(this->shared_from_this(), ddVariablePair.first, {unprimed}));
             variablesPrime.emplace_back(Bdd<DdType::CUDD>(this->shared_from_this(), ddVariablePair.second, {primed}));
             
-            metaVariableMap.emplace(unprimed, DdMetaVariable<LibraryType>(name, variables, this->shared_from_this()));
-            metaVariableMap.emplace(primed, DdMetaVariable<LibraryType>(name + "'", variablesPrime, this->shared_from_this()));
+            metaVariableMap.emplace(unprimed, DdMetaVariable<LibraryType>(name, variables));
+            metaVariableMap.emplace(primed, DdMetaVariable<LibraryType>(name + "'", variablesPrime));
             
             return std::make_pair(unprimed, primed);
         }
diff --git a/src/storage/dd/DdManager.h b/src/storage/dd/DdManager.h
index 6d7dcc5be..d4f23fdfd 100644
--- a/src/storage/dd/DdManager.h
+++ b/src/storage/dd/DdManager.h
@@ -8,6 +8,7 @@
 #include "src/storage/dd/DdMetaVariable.h"
 #include "src/storage/dd/Bdd.h"
 #include "src/storage/dd/Add.h"
+#include "src/storage/dd/AddIterator.h"
 
 #include "src/storage/expressions/Variable.h"
 
@@ -15,12 +16,17 @@
 
 namespace storm {
     namespace dd {
+        template<DdType LibraryType>
+        class Odd;
+        
         // Declare DdManager class so we can then specialize it for the different DD types.
         template<DdType LibraryType>
         class DdManager : public std::enable_shared_from_this<DdManager<LibraryType>> {
         public:
             friend class Bdd<LibraryType>;
             friend class Add<LibraryType, double>;
+            friend class AddIterator<LibraryType, double>;
+            friend class Odd<LibraryType>;
             
             /*!
              * Creates an empty manager without any meta variables.
diff --git a/src/storage/dd/DdMetaVariable.h b/src/storage/dd/DdMetaVariable.h
index 2e92c34c7..c9f426f38 100644
--- a/src/storage/dd/DdMetaVariable.h
+++ b/src/storage/dd/DdMetaVariable.h
@@ -5,6 +5,7 @@
 
 #include "src/storage/dd/DdType.h"
 #include "src/storage/dd/Bdd.h"
+#include "src/storage/dd/AddIterator.h"
 
 namespace storm {
     namespace dd {
@@ -23,7 +24,12 @@ namespace storm {
         public:
             friend class DdManager<LibraryType>;
             friend class Bdd<LibraryType>;
-            friend class Add<LibraryType, double>;
+
+            template <DdType LibraryTypePrime, typename ValueTypePrime>
+            friend class Add;
+
+            template <DdType LibraryTypePrime, typename ValueTypePrime>
+            friend class AddIterator;
             
             /*!
              * Retrieves the name of the meta variable.
diff --git a/src/storage/dd/cudd/CuddAddIterator.cpp b/src/storage/dd/cudd/CuddAddIterator.cpp
index e19d9396e..070a3982d 100644
--- a/src/storage/dd/cudd/CuddAddIterator.cpp
+++ b/src/storage/dd/cudd/CuddAddIterator.cpp
@@ -1,5 +1,5 @@
 #include "src/storage/dd/cudd/CuddAddIterator.h"
-#include "src/storage/dd/cudd/CuddDdManager.h"
+#include "src/storage/dd/DdManager.h"
 #include "src/storage/dd/DdMetaVariable.h"
 #include "src/utility/macros.h"
 #include "src/storage/expressions/ExpressionManager.h"
@@ -7,12 +7,12 @@
 namespace storm {
     namespace dd {
         template<typename ValueType>
-        AddIterator<DdType::CUDD, ValueType>::DdForwardIterator() : ddManager(), generator(), cube(), value(), isAtEnd(), metaVariables(), enumerateDontCareMetaVariables(), cubeCounter(), relevantDontCareDdVariables(), currentValuation() {
+        AddIterator<DdType::CUDD, ValueType>::AddIterator() : ddManager(), generator(), cube(), value(), isAtEnd(), metaVariables(), enumerateDontCareMetaVariables(), cubeCounter(), relevantDontCareDdVariables(), currentValuation() {
             // Intentionally left empty.
         }
         
         template<typename ValueType>
-        AddIterator<DdType::CUDD, ValueType>::DdForwardIterator(std::shared_ptr<DdManager<DdType::CUDD> const> ddManager, DdGen* generator, int* cube, double value, bool isAtEnd, std::set<storm::expressions::Variable> const* metaVariables, bool enumerateDontCareMetaVariables) : ddManager(ddManager), generator(generator), cube(cube), value(value), isAtEnd(isAtEnd), metaVariables(metaVariables), enumerateDontCareMetaVariables(enumerateDontCareMetaVariables), cubeCounter(), relevantDontCareDdVariables(), currentValuation(ddManager->getExpressionManager().getSharedPointer()) {
+        AddIterator<DdType::CUDD, ValueType>::AddIterator(std::shared_ptr<DdManager<DdType::CUDD> const> ddManager, DdGen* generator, int* cube, double value, bool isAtEnd, std::set<storm::expressions::Variable> const* metaVariables, bool enumerateDontCareMetaVariables) : ddManager(ddManager), generator(generator), cube(cube), value(value), isAtEnd(isAtEnd), metaVariables(metaVariables), enumerateDontCareMetaVariables(enumerateDontCareMetaVariables), cubeCounter(), relevantDontCareDdVariables(), currentValuation(ddManager->getExpressionManager().getSharedPointer()) {
             // If the given generator is not yet at its end, we need to create the current valuation from the cube from
             // scratch.
             if (!this->isAtEnd) {
@@ -22,7 +22,7 @@ namespace storm {
         }
         
         template<typename ValueType>
-        AddIterator<DdType::CUDD, ValueType>::DdForwardIterator(AddIterator<DdType::CUDD, ValueType>&& other) : ddManager(other.ddManager), generator(other.generator), cube(other.cube), value(other.value), isAtEnd(other.isAtEnd), metaVariables(other.metaVariables), cubeCounter(other.cubeCounter), relevantDontCareDdVariables(other.relevantDontCareDdVariables), currentValuation(other.currentValuation) {
+        AddIterator<DdType::CUDD, ValueType>::AddIterator(AddIterator<DdType::CUDD, ValueType>&& other) : ddManager(other.ddManager), generator(other.generator), cube(other.cube), value(other.value), isAtEnd(other.isAtEnd), metaVariables(other.metaVariables), cubeCounter(other.cubeCounter), relevantDontCareDdVariables(other.relevantDontCareDdVariables), currentValuation(other.currentValuation) {
             // Null-out the pointers of which we took possession.
             other.cube = nullptr;
             other.generator = nullptr;
@@ -49,7 +49,7 @@ namespace storm {
         }
         
         template<typename ValueType>
-        AddIterator<DdType::CUDD, ValueType>::~DdForwardIterator() {
+        AddIterator<DdType::CUDD, ValueType>::~AddIterator() {
             // We free the pointers sind Cudd allocates them using malloc rather than new/delete.
             if (this->cube != nullptr) {
                 free(this->cube);
@@ -89,7 +89,7 @@ namespace storm {
             
             for (uint_fast64_t index = 0; index < this->relevantDontCareDdVariables.size(); ++index) {
                 auto const& ddMetaVariable = this->ddManager->getMetaVariable(std::get<0>(this->relevantDontCareDdVariables[index]));
-                if (ddMetaVariable.getType() == DdMetaVariable<DdType::CUDD>::MetaVariableType::Bool) {
+                if (ddMetaVariable.getType() == MetaVariableType::Bool) {
                     if ((this->cubeCounter & (1ull << index)) != 0) {
                         currentValuation.setBooleanValue(std::get<0>(this->relevantDontCareDdVariables[index]), true);
                     } else {
@@ -117,7 +117,7 @@ namespace storm {
                 bool metaVariableAppearsInCube = false;
                 std::vector<std::tuple<storm::expressions::Variable, uint_fast64_t>> localRelenvantDontCareDdVariables;
                 auto const& ddMetaVariable = this->ddManager->getMetaVariable(metaVariable);
-                if (ddMetaVariable.getType() == DdMetaVariable<DdType::CUDD>::MetaVariableType::Bool) {
+                if (ddMetaVariable.getType() == MetaVariableType::Bool) {
                     if (this->cube[ddMetaVariable.getDdVariables().front().getIndex()] == 0) {
                         metaVariableAppearsInCube = true;
                         currentValuation.setBooleanValue(metaVariable, false);
diff --git a/src/storage/dd/cudd/CuddAddIterator.h b/src/storage/dd/cudd/CuddAddIterator.h
index 262667195..577c1695f 100644
--- a/src/storage/dd/cudd/CuddAddIterator.h
+++ b/src/storage/dd/cudd/CuddAddIterator.h
@@ -20,12 +20,12 @@ namespace storm {
         class DdManager;
         
         template<DdType Type, typename ValueType>
-        class Add;
+        class InternalAdd;
         
         template<typename ValueType>
         class AddIterator<DdType::CUDD, ValueType> {
         public:
-            friend class Add<DdType::CUDD, ValueType>;
+            friend class InternalAdd<DdType::CUDD, ValueType>;
 
             // Default-instantiate the constructor.
             AddIterator();
diff --git a/src/storage/dd/cudd/CuddOdd.cpp b/src/storage/dd/cudd/CuddOdd.cpp
index fe38a2c48..0e238e1ff 100644
--- a/src/storage/dd/cudd/CuddOdd.cpp
+++ b/src/storage/dd/cudd/CuddOdd.cpp
@@ -8,8 +8,8 @@
 #include "src/exceptions/InvalidArgumentException.h"
 #include "src/utility/macros.h"
 
-#include "src/storage/dd/cudd/CuddDdManager.h"
-#include "src/storage/dd/cudd/CuddDdMetaVariable.h"
+#include "src/storage/dd/DdManager.h"
+#include "src/storage/dd/DdMetaVariable.h"
 
 namespace storm {
     namespace dd {
@@ -23,7 +23,7 @@ namespace storm {
             std::vector<std::unordered_map<DdNode*, std::shared_ptr<Odd<DdType::CUDD>>>> uniqueTableForLevels(ddVariableIndices.size() + 1);
             
             // Now construct the ODD structure from the ADD.
-            std::shared_ptr<Odd<DdType::CUDD>> rootOdd = buildOddFromAddRec(add.getCuddDdNode(), manager->getCuddManager(), 0, ddVariableIndices.size(), ddVariableIndices, uniqueTableForLevels);
+            std::shared_ptr<Odd<DdType::CUDD>> rootOdd = buildOddFromAddRec(add.internalAdd.getCuddDdNode(), manager->internalDdManager.getCuddManager(), 0, ddVariableIndices.size(), ddVariableIndices, uniqueTableForLevels);
             
             // Finally, move the children of the root ODD into this ODD.
             this->elseNode = std::move(rootOdd->elseNode);
@@ -42,7 +42,7 @@ namespace storm {
             std::vector<std::unordered_map<std::pair<DdNode*, bool>, std::shared_ptr<Odd<DdType::CUDD>>, HashFunctor>> uniqueTableForLevels(ddVariableIndices.size() + 1);
             
             // Now construct the ODD structure from the BDD.
-            std::shared_ptr<Odd<DdType::CUDD>> rootOdd = buildOddFromBddRec(Cudd_Regular(bdd.getCuddDdNode()), manager->getCuddManager(), 0, Cudd_IsComplement(bdd.getCuddDdNode()), ddVariableIndices.size(), ddVariableIndices, uniqueTableForLevels);
+            std::shared_ptr<Odd<DdType::CUDD>> rootOdd = buildOddFromBddRec(Cudd_Regular(bdd.getCuddDdNode()), manager->internalDdManager.getCuddManager(), 0, Cudd_IsComplement(bdd.getCuddDdNode()), ddVariableIndices.size(), ddVariableIndices, uniqueTableForLevels);
             
             // Finally, move the children of the root ODD into this ODD.
             this->elseNode = std::move(rootOdd->elseNode);
diff --git a/src/storage/dd/cudd/InternalCuddAdd.cpp b/src/storage/dd/cudd/InternalCuddAdd.cpp
index 9b19ce73f..0b9d0f6dd 100644
--- a/src/storage/dd/cudd/InternalCuddAdd.cpp
+++ b/src/storage/dd/cudd/InternalCuddAdd.cpp
@@ -39,6 +39,7 @@ namespace storm {
         template<typename ValueType>
         InternalAdd<DdType::CUDD, ValueType>& InternalAdd<DdType::CUDD, ValueType>::operator|=(InternalAdd<DdType::CUDD, ValueType> const& other) {
             this->cuddAdd = this->getCuddAdd() | other.getCuddAdd();
+            return *this;
         }
         
         template<typename ValueType>
@@ -49,6 +50,7 @@ namespace storm {
         template<typename ValueType>
         InternalAdd<DdType::CUDD, ValueType>& InternalAdd<DdType::CUDD, ValueType>::operator+=(InternalAdd<DdType::CUDD, ValueType> const& other) {
             this->cuddAdd = this->getCuddAdd() + other.getCuddAdd();
+            return *this;
         }
         
         template<typename ValueType>
@@ -59,6 +61,7 @@ namespace storm {
         template<typename ValueType>
         InternalAdd<DdType::CUDD, ValueType>& InternalAdd<DdType::CUDD, ValueType>::operator*=(InternalAdd<DdType::CUDD, ValueType> const& other) {
             this->cuddAdd = this->getCuddAdd() * other.getCuddAdd();
+            return *this;
         }
         
         template<typename ValueType>
@@ -69,16 +72,18 @@ namespace storm {
         template<typename ValueType>
         InternalAdd<DdType::CUDD, ValueType>& InternalAdd<DdType::CUDD, ValueType>::operator-=(InternalAdd<DdType::CUDD, ValueType> const& other) {
             this->cuddAdd = this->getCuddAdd() - other.getCuddAdd();
+            return *this;
         }
         
         template<typename ValueType>
         InternalAdd<DdType::CUDD, ValueType> InternalAdd<DdType::CUDD, ValueType>::operator/(InternalAdd<DdType::CUDD, ValueType> const& other) const {
-            return InternalAdd<DdType::CUDD, ValueType>(ddManager, this->getCuddAdd() / other.getCuddAdd());
+            return InternalAdd<DdType::CUDD, ValueType>(ddManager, this->getCuddAdd().Divide(other.getCuddAdd()));
         }
         
         template<typename ValueType>
         InternalAdd<DdType::CUDD, ValueType>& InternalAdd<DdType::CUDD, ValueType>::operator/=(InternalAdd<DdType::CUDD, ValueType> const& other) {
-            this->cuddAdd = this->getCuddAdd() / other.getCuddAdd();
+            this->cuddAdd = this->getCuddAdd().Divide(other.getCuddAdd());
+            return *this;
         }
         
         template<typename ValueType>
@@ -148,17 +153,17 @@ namespace storm {
         
         template<typename ValueType>
         InternalAdd<DdType::CUDD, ValueType> InternalAdd<DdType::CUDD, ValueType>::sumAbstract(InternalBdd<DdType::CUDD> const& cube) const {
-            return InternalAdd<DdType::CUDD, ValueType>(ddManager, this->getCuddAdd().ExistAbstract(cube.getCuddBdd()));
+            return InternalAdd<DdType::CUDD, ValueType>(ddManager, this->getCuddAdd().ExistAbstract(cube.toAdd<ValueType>().getCuddAdd()));
         }
         
         template<typename ValueType>
         InternalAdd<DdType::CUDD, ValueType> InternalAdd<DdType::CUDD, ValueType>::minAbstract(InternalBdd<DdType::CUDD> const& cube) const {
-            return InternalAdd<DdType::CUDD, ValueType>(ddManager, this->getCuddAdd().MinAbstract(cube.getCuddBdd()));
+            return InternalAdd<DdType::CUDD, ValueType>(ddManager, this->getCuddAdd().MinAbstract(cube.toAdd<ValueType>().getCuddAdd()));
         }
         
         template<typename ValueType>
         InternalAdd<DdType::CUDD, ValueType> InternalAdd<DdType::CUDD, ValueType>::maxAbstract(InternalBdd<DdType::CUDD> const& cube) const {
-            return InternalAdd<DdType::CUDD, ValueType>(ddManager, this->getCuddAdd().MaxAbstract(cube.getCuddBdd()));
+            return InternalAdd<DdType::CUDD, ValueType>(ddManager, this->getCuddAdd().MaxAbstract(cube.toAdd<ValueType>().getCuddAdd()));
         }
         
         template<typename ValueType>
@@ -178,7 +183,7 @@ namespace storm {
                 fromAdd.push_back(it1->getCuddAdd());
                 toAdd.push_back(it2->getCuddAdd());
             }
-            return InternalBdd<DdType::CUDD>(ddManager, this->getCuddBdd().SwapVariables(fromAdd, toAdd));
+            return InternalAdd<DdType::CUDD, ValueType>(ddManager, this->getCuddAdd().SwapVariables(fromAdd, toAdd));
         }
         
         template<typename ValueType>
@@ -186,7 +191,7 @@ namespace storm {
             // Create the CUDD summation variables.
             std::vector<ADD> summationAdds;
             for (auto const& ddVariable : summationDdVariables) {
-                summationAdds.push_back(ddVariable.toAdd().getCuddAdd());
+                summationAdds.push_back(ddVariable.getCuddAdd());
             }
             
             return InternalAdd<DdType::CUDD, ValueType>(ddManager, this->getCuddAdd().MatrixMultiply(otherMatrix.getCuddAdd(), summationAdds));
@@ -302,7 +307,7 @@ namespace storm {
             // Open the file, dump the DD and close it again.
             FILE* filePointer = fopen(filename.c_str() , "w");
             std::vector<ADD> cuddAddVector = { this->getCuddAdd() };
-            this->getDdManager()->getCuddManager().DumpDot(cuddAddVector, &ddVariableNames[0], &ddNames[0], filePointer);
+            ddManager->getCuddManager().DumpDot(cuddAddVector, &ddVariableNames[0], &ddNames[0], filePointer);
             fclose(filePointer);
             
             // Finally, delete the names.
@@ -315,16 +320,16 @@ namespace storm {
         }
         
         template<typename ValueType>
-        AddIterator<DdType::CUDD, ValueType> InternalAdd<DdType::CUDD, ValueType>::begin(std::set<storm::expressions::Variable> const& metaVariables, bool enumerateDontCareMetaVariables) const {
+        AddIterator<DdType::CUDD, ValueType> InternalAdd<DdType::CUDD, ValueType>::begin(std::shared_ptr<DdManager<DdType::CUDD> const> fullDdManager, std::set<storm::expressions::Variable> const& metaVariables, bool enumerateDontCareMetaVariables) const {
             int* cube;
             double value;
             DdGen* generator = this->getCuddAdd().FirstCube(&cube, &value);
-            return AddIterator<DdType::CUDD, ValueType>(ddManager, generator, cube, value, (Cudd_IsGenEmpty(generator) != 0), &metaVariables, enumerateDontCareMetaVariables);
+            return AddIterator<DdType::CUDD, ValueType>(fullDdManager, generator, cube, value, (Cudd_IsGenEmpty(generator) != 0), &metaVariables, enumerateDontCareMetaVariables);
         }
         
         template<typename ValueType>
-        AddIterator<DdType::CUDD, ValueType> InternalAdd<DdType::CUDD, ValueType>::end(bool enumerateDontCareMetaVariables) const {
-            return AddIterator<DdType::CUDD, ValueType>(ddManager, nullptr, nullptr, 0, true, nullptr, enumerateDontCareMetaVariables);
+        AddIterator<DdType::CUDD, ValueType> InternalAdd<DdType::CUDD, ValueType>::end(std::shared_ptr<DdManager<DdType::CUDD> const> fullDdManager, bool enumerateDontCareMetaVariables) const {
+            return AddIterator<DdType::CUDD, ValueType>(fullDdManager, nullptr, nullptr, 0, true, nullptr, enumerateDontCareMetaVariables);
         }
         
         template<typename ValueType>
@@ -404,10 +409,10 @@ namespace storm {
         }
         
         template<typename ValueType>
-        storm::storage::SparseMatrix<ValueType> InternalAdd<DdType::CUDD, ValueType>::toMatrix(storm::dd::Odd<DdType::CUDD> const& rowOdd, std::vector<uint_fast64_t> const& ddRowVariableIndices, storm::dd::Odd<DdType::CUDD> const& columnOdd, std::vector<uint_fast64_t> const& ddColumnVariableIndices) const {
+        storm::storage::SparseMatrix<ValueType> InternalAdd<DdType::CUDD, ValueType>::toMatrix(uint_fast64_t numberOfDdVariables, storm::dd::Odd<DdType::CUDD> const& rowOdd, std::vector<uint_fast64_t> const& ddRowVariableIndices, storm::dd::Odd<DdType::CUDD> const& columnOdd, std::vector<uint_fast64_t> const& ddColumnVariableIndices) const {
             // Prepare the vectors that represent the matrix.
             std::vector<uint_fast64_t> rowIndications(rowOdd.getTotalOffset() + 1);
-            std::vector<storm::storage::MatrixEntry<uint_fast64_t, double>> columnsAndValues(this->getNonZeroCount());
+            std::vector<storm::storage::MatrixEntry<uint_fast64_t, double>> columnsAndValues(this->getNonZeroCount(numberOfDdVariables));
             
             // Create a trivial row grouping.
             std::vector<uint_fast64_t> trivialRowGroupIndices(rowIndications.size());
@@ -450,7 +455,7 @@ namespace storm {
         template<typename ValueType>
         void InternalAdd<DdType::CUDD, ValueType>::toMatrixRec(DdNode const* dd, std::vector<uint_fast64_t>& rowIndications, std::vector<storm::storage::MatrixEntry<uint_fast64_t, double>>& columnsAndValues, std::vector<uint_fast64_t> const& rowGroupOffsets, Odd<DdType::CUDD> const& rowOdd, Odd<DdType::CUDD> const& columnOdd, uint_fast64_t currentRowLevel, uint_fast64_t currentColumnLevel, uint_fast64_t maxLevel, uint_fast64_t currentRowOffset, uint_fast64_t currentColumnOffset, std::vector<uint_fast64_t> const& ddRowVariableIndices, std::vector<uint_fast64_t> const& ddColumnVariableIndices, bool generateValues) const {
             // For the empty DD, we do not need to add any entries.
-            if (dd == Cudd_ReadZero(this->getDdManager()->getCuddManager().getManager())) {
+            if (dd == Cudd_ReadZero(ddManager->getCuddManager().getManager())) {
                 return;
             }
             
@@ -503,10 +508,9 @@ namespace storm {
         template<typename ValueType>
         storm::storage::SparseMatrix<ValueType> InternalAdd<DdType::CUDD, ValueType>::toMatrix(std::vector<uint_fast64_t> const& ddGroupVariableIndices, InternalBdd<DdType::CUDD> const& groupVariableCube, storm::dd::Odd<DdType::CUDD> const& rowOdd, std::vector<uint_fast64_t> const& ddRowVariableIndices, storm::dd::Odd<DdType::CUDD> const& columnOdd, std::vector<uint_fast64_t> const& ddColumnVariableIndices, InternalBdd<DdType::CUDD> const& columnVariableCube) const {
             // Start by computing the offsets (in terms of rows) for each row group.
-            InternalAdd<DdType::CUDD, ValueType> stateToNumberOfChoices = this->notZero().existsAbstract(columnVariableCube).toAdd().sumAbstract(groupVariableCube);
-            std::vector<ValueType> rowGroupIndicesAsValueType = stateToNumberOfChoices.toVector(rowOdd);
-            std::vector<uint_fast64_t> rowGroupIndices(rowGroupIndicesAsValueType.size() + 1);
-            std::transform(rowGroupIndicesAsValueType.begin(), rowGroupIndicesAsValueType.end(), rowGroupIndices.begin(), [] (ValueType const& value) { return static_cast<uint_fast64_t>(value); });
+            InternalAdd<DdType::CUDD, uint_fast64_t> stateToNumberOfChoices = this->notZero().existsAbstract(columnVariableCube).template toAdd<uint_fast64_t>().sumAbstract(groupVariableCube);
+            std::vector<ValueType> rowGroupIndices = stateToNumberOfChoices.toVector(rowOdd);
+            rowGroupIndices.resize(rowGroupIndices.size() + 1);
             uint_fast64_t tmp = 0;
             uint_fast64_t tmp2 = 0;
             for (uint_fast64_t i = 1; i < rowGroupIndices.size(); ++i) {
@@ -540,7 +544,7 @@ namespace storm {
             }
             
             // Since we modified the rowGroupIndices, we need to restore the correct values.
-            std::function<uint_fast64_t (uint_fast64_t const&, double const&)> fct = [] (uint_fast64_t const& a, double const& b) -> uint_fast64_t { return a - static_cast<uint_fast64_t>(b); };
+            std::function<uint_fast64_t (uint_fast64_t const&, uint_fast64_t const&)> fct = [] (uint_fast64_t const& a, double const& b) -> uint_fast64_t { return a - static_cast<uint_fast64_t>(b); };
             composeVectorRec(stateToRowGroupCount.getCuddDdNode(), 0, ddRowVariableIndices.size(), 0, rowOdd, ddRowVariableIndices, rowGroupIndices, fct);
             
             // Now that we computed the number of entries in each row, compute the corresponding offsets in the entry vector.
diff --git a/src/storage/dd/cudd/InternalCuddAdd.h b/src/storage/dd/cudd/InternalCuddAdd.h
index 8b0fd3dbe..bfb9f1897 100644
--- a/src/storage/dd/cudd/InternalCuddAdd.h
+++ b/src/storage/dd/cudd/InternalCuddAdd.h
@@ -23,6 +23,9 @@ namespace storm {
     }
     
     namespace dd {
+        template<DdType LibraryType>
+        class DdManager;
+
         template<DdType LibraryType>
         class InternalDdManager;
         
@@ -486,7 +489,7 @@ namespace storm {
              * if a meta variable does not at all influence the the function value.
              * @return An iterator that points to the first meta variable assignment with a non-zero function value.
              */
-            AddIterator<DdType::CUDD, ValueType> begin(std::set<storm::expressions::Variable> const& metaVariables, bool enumerateDontCareMetaVariables = true) const;
+            AddIterator<DdType::CUDD, ValueType> begin(std::shared_ptr<DdManager<DdType::CUDD> const> fullDdManager, std::set<storm::expressions::Variable> const& metaVariables, bool enumerateDontCareMetaVariables = true) const;
             
             /*!
              * Retrieves an iterator that points past the end of the container.
@@ -495,7 +498,7 @@ namespace storm {
              * if a meta variable does not at all influence the the function value.
              * @return An iterator that points past the end of the container.
              */
-             AddIterator<DdType::CUDD, ValueType> end(bool enumerateDontCareMetaVariables = true) const;
+             AddIterator<DdType::CUDD, ValueType> end(std::shared_ptr<DdManager<DdType::CUDD> const> fullDdManager, bool enumerateDontCareMetaVariables = true) const;
             
             /*!
              * Converts the ADD to a vector. The given offset-labeled DD is used to determine the correct row of
@@ -510,7 +513,7 @@ namespace storm {
             
             void composeVector(storm::dd::Odd<DdType::CUDD> const& odd, std::vector<uint_fast64_t> const& ddVariableIndices, std::vector<ValueType>& targetVector, std::function<ValueType (ValueType const&, ValueType const&)> const& function) const;
             
-            storm::storage::SparseMatrix<ValueType> toMatrix(storm::dd::Odd<DdType::CUDD> const& rowOdd, std::vector<uint_fast64_t> const& ddRowVariableIndices, storm::dd::Odd<DdType::CUDD> const& columnOdd, std::vector<uint_fast64_t> const& ddColumnVariableIndices) const;
+            storm::storage::SparseMatrix<ValueType> toMatrix(uint_fast64_t numberOfDdVariables, storm::dd::Odd<DdType::CUDD> const& rowOdd, std::vector<uint_fast64_t> const& ddRowVariableIndices, storm::dd::Odd<DdType::CUDD> const& columnOdd, std::vector<uint_fast64_t> const& ddColumnVariableIndices) const;
             
             storm::storage::SparseMatrix<ValueType> toMatrix(std::vector<uint_fast64_t> const& ddGroupVariableIndices, InternalBdd<DdType::CUDD> const& groupVariableCube, storm::dd::Odd<DdType::CUDD> const& rowOdd, std::vector<uint_fast64_t> const& ddRowVariableIndices, storm::dd::Odd<DdType::CUDD> const& columnOdd, std::vector<uint_fast64_t> const& ddColumnVariableIndices, InternalBdd<DdType::CUDD> const& columnVariableCube) const;
             
diff --git a/src/storage/dd/cudd/InternalCuddBdd.cpp b/src/storage/dd/cudd/InternalCuddBdd.cpp
index 9320ef406..8e53d9573 100644
--- a/src/storage/dd/cudd/InternalCuddBdd.cpp
+++ b/src/storage/dd/cudd/InternalCuddBdd.cpp
@@ -1,6 +1,9 @@
 #include "src/storage/dd/cudd/InternalCuddBdd.h"
 
 #include "src/storage/dd/cudd/InternalCuddDdManager.h"
+#include "src/storage/dd/cudd/CuddOdd.h"
+
+#include "src/storage/BitVector.h"
 
 namespace storm {
     namespace dd {
@@ -228,10 +231,9 @@ namespace storm {
             }
         }
         
-        storm::storage::BitVector InternalBdd<DdType::CUDD>::toVector(storm::dd::Odd<DdType::CUDD> const& rowOdd) const {
-            std::vector<uint_fast64_t> ddVariableIndices = this->getSortedVariableIndices();
+        storm::storage::BitVector InternalBdd<DdType::CUDD>::toVector(storm::dd::Odd<DdType::CUDD> const& rowOdd, std::vector<uint_fast64_t> const& ddVariableIndices) const {
             storm::storage::BitVector result(rowOdd.getTotalOffset());
-            this->toVectorRec(this->getCuddDdNode(), this->getDdManager()->getCuddManager(), result, rowOdd, Cudd_IsComplement(this->getCuddDdNode()), 0, ddVariableIndices.size(), 0, ddVariableIndices);
+            this->toVectorRec(this->getCuddDdNode(), ddManager->getCuddManager(), result, rowOdd, Cudd_IsComplement(this->getCuddDdNode()), 0, ddVariableIndices.size(), 0, ddVariableIndices);
             return result;
         }
         
diff --git a/src/storage/dd/cudd/InternalCuddBdd.h b/src/storage/dd/cudd/InternalCuddBdd.h
index b627e7912..1fa776c3f 100644
--- a/src/storage/dd/cudd/InternalCuddBdd.h
+++ b/src/storage/dd/cudd/InternalCuddBdd.h
@@ -288,7 +288,7 @@ namespace storm {
              * @param rowOdd The ODD used for determining the correct row.
              * @return The bit vector that is represented by this BDD.
              */
-            storm::storage::BitVector toVector(storm::dd::Odd<DdType::CUDD> const& rowOdd) const;
+            storm::storage::BitVector toVector(storm::dd::Odd<DdType::CUDD> const& rowOdd, std::vector<uint_fast64_t> const& ddVariableIndices) const;
             
         private:
             /*!
diff --git a/src/storage/dd/cudd/InternalCuddDdManager.h b/src/storage/dd/cudd/InternalCuddDdManager.h
index a83b03bc2..a967ca0dd 100644
--- a/src/storage/dd/cudd/InternalCuddDdManager.h
+++ b/src/storage/dd/cudd/InternalCuddDdManager.h
@@ -16,12 +16,16 @@ namespace storm {
 
         template<DdType LibraryType>
         class InternalBdd;
+
+        template<DdType LibraryType>
+        class Odd;
         
         template<>
         class InternalDdManager<DdType::CUDD> {
         public:
             friend class InternalAdd<DdType::CUDD, double>;
             friend class InternalBdd<DdType::CUDD>;
+            friend class Odd<DdType::CUDD>;
             
             /*!
              * Creates a new internal manager for CUDD DDs.