diff --git a/src/storm/generator/PrismNextStateGenerator.cpp b/src/storm/generator/PrismNextStateGenerator.cpp
index 26c9bf673..a9c845d32 100644
--- a/src/storm/generator/PrismNextStateGenerator.cpp
+++ b/src/storm/generator/PrismNextStateGenerator.cpp
@@ -296,16 +296,16 @@ namespace storm {
             std::vector<Choice<ValueType>> allChoices;
             if (this->getOptions().isApplyMaximalProgressAssumptionSet()) {
                 // First explore only edges without a rate
-                allChoices = getUnlabeledChoices(*this->state, stateToIdCallback, CommandFilter::Probabilistic);
-                addLabeledChoices(allChoices, *this->state, stateToIdCallback, CommandFilter::Probabilistic);
+                allChoices = getAsynchronousChoices(*this->state, stateToIdCallback, CommandFilter::Probabilistic);
+                addSynchronousChoices(allChoices, *this->state, stateToIdCallback, CommandFilter::Probabilistic);
                 if (allChoices.empty()) {
                     // Expand the Markovian edges if there are no probabilistic ones.
-                    allChoices = getUnlabeledChoices(*this->state, stateToIdCallback, CommandFilter::Markovian);
-                    addLabeledChoices(allChoices, *this->state, stateToIdCallback, CommandFilter::Markovian);
+                    allChoices = getAsynchronousChoices(*this->state, stateToIdCallback, CommandFilter::Markovian);
+                    addSynchronousChoices(allChoices, *this->state, stateToIdCallback, CommandFilter::Markovian);
                 }
             } else {
-                allChoices = getUnlabeledChoices(*this->state, stateToIdCallback);
-                addLabeledChoices(allChoices, *this->state, stateToIdCallback);
+                allChoices = getAsynchronousChoices(*this->state, stateToIdCallback);
+                addSynchronousChoices(allChoices, *this->state, stateToIdCallback);
             }
 
             std::size_t totalNumberOfChoices = allChoices.size();
@@ -538,7 +538,7 @@ namespace storm {
         }
 
         template<typename ValueType, typename StateType>
-        std::vector<Choice<ValueType>> PrismNextStateGenerator<ValueType, StateType>::getUnlabeledChoices(CompressedState const& state, StateToIdCallback stateToIdCallback, CommandFilter const& commandFilter) {
+        std::vector<Choice<ValueType>> PrismNextStateGenerator<ValueType, StateType>::getAsynchronousChoices(CompressedState const& state, StateToIdCallback stateToIdCallback, CommandFilter const& commandFilter) {
             std::vector<Choice<ValueType>> result;
 
             // Iterate over all modules.
@@ -650,7 +650,7 @@ namespace storm {
         }
 
         template<typename ValueType, typename StateType>
-        void PrismNextStateGenerator<ValueType, StateType>::addLabeledChoices(std::vector<Choice<ValueType>>& choices, CompressedState const& state, StateToIdCallback stateToIdCallback, CommandFilter const& commandFilter) {
+        void PrismNextStateGenerator<ValueType, StateType>::addSynchronousChoices(std::vector<Choice<ValueType>>& choices, CompressedState const& state, StateToIdCallback stateToIdCallback, CommandFilter const& commandFilter) {
 
             for (uint_fast64_t actionIndex : program.getSynchronizingActionIndices()) {
                 if (this->actionMask != nullptr) {
diff --git a/src/storm/generator/PrismNextStateGenerator.h b/src/storm/generator/PrismNextStateGenerator.h
index a053e4488..a83d0bc31 100644
--- a/src/storm/generator/PrismNextStateGenerator.h
+++ b/src/storm/generator/PrismNextStateGenerator.h
@@ -86,21 +86,22 @@ namespace storm {
             boost::optional<std::vector<std::vector<std::reference_wrapper<storm::prism::Command const>>>> getActiveCommandsByActionIndex(uint_fast64_t const& actionIndex, CommandFilter const& commandFilter = CommandFilter::All);
             
             /*!
-             * Retrieves all unlabeled choices possible from the given state.
+             * Retrieves all choices that are definitively asynchronous, possible from the given state.
              *
              * @param state The state for which to retrieve the unlabeled choices.
-             * @return The unlabeled choices of the state.
+             * @return The asynchronous choices of the state.
              */
-            std::vector<Choice<ValueType>> getUnlabeledChoices(CompressedState const& state, StateToIdCallback stateToIdCallback, CommandFilter const& commandFilter = CommandFilter::All);
+            std::vector<Choice<ValueType>> getAsynchronousChoices(CompressedState const& state, StateToIdCallback stateToIdCallback, CommandFilter const& commandFilter = CommandFilter::All);
             
             /*!
-             * Retrieves all labeled choices possible from the given state.
+             * Retrieves all (potentially) synchronous choices possible from the given state. 
+             * Note that these may include choices that run asynchronously for this state.
              *
              * @param choices The new choices are inserted in this vector
              * @param state The state for which to retrieve the unlabeled choices.
-             * @return The labeled choices of the state.
+             * @return The synchronous choices of the state.
              */
-            void addLabeledChoices(std::vector<Choice<ValueType>>& choices, CompressedState const& state, StateToIdCallback stateToIdCallback, CommandFilter const& commandFilter = CommandFilter::All);
+            void addSynchronousChoices(std::vector<Choice<ValueType>>& choices, CompressedState const& state, StateToIdCallback stateToIdCallback, CommandFilter const& commandFilter = CommandFilter::All);
 
             /*!
              * Extend the Json struct with additional information about the state.
diff --git a/src/storm/storage/prism/Program.h b/src/storm/storage/prism/Program.h
index afca86cb4..1c090107b 100644
--- a/src/storm/storage/prism/Program.h
+++ b/src/storm/storage/prism/Program.h
@@ -708,8 +708,14 @@ namespace storm {
              */
             Program flattenModules(std::shared_ptr<storm::utility::solver::SmtSolverFactory> const& smtSolverFactory = std::shared_ptr<storm::utility::solver::SmtSolverFactory>(new storm::utility::solver::SmtSolverFactory())) const;
 
-
-            Program labelUnlabelledCommands(std::map<uint64_t,std::string> const& nameSuggestions) const;
+            /*!
+             * Give commands that do not have an action name an action,
+             * which can be helpful for debugging and understanding traces.
+             *
+             * @param nameSuggestions Optional suggestions that map command indices to names
+             * @return
+             */
+            Program labelUnlabelledCommands(std::map<uint64_t,std::string> const& nameSuggestions = {}) const;
 
 
             friend std::ostream& operator<<(std::ostream& stream, Program const& program);