diff --git a/src/utility/shortestPaths.cpp b/src/utility/shortestPaths.cpp
index ac868070d..409030c32 100644
--- a/src/utility/shortestPaths.cpp
+++ b/src/utility/shortestPaths.cpp
@@ -8,12 +8,11 @@ namespace storm {
         namespace ksp {
             template <typename T>
             ShortestPathsGenerator<T>::ShortestPathsGenerator(std::shared_ptr<models::sparse::Model<T>> model,
-                                                              state_list_t const& targets) : model(model), targets(targets) {
-                // FIXME: does this create a copy? I don't need one, so I should avoid that
-                transitionMatrix = model->getTransitionMatrix();
-                numStates = model->getNumberOfStates() + 1; // one more for meta-target
-
-                metaTarget = numStates - 1; // first unused state number
+                    state_list_t const& targets) : transitionMatrix(model->getTransitionMatrix()),
+                                                   numStates(model->getNumberOfStates() + 1), // one more for meta-target
+                                                   metaTarget(model->getNumberOfStates()), // first unused state number
+                                                   initialStates(model->getInitialStates()),
+                                                   targets(targets) {
                 targetSet = std::unordered_set<state_t>(targets.begin(), targets.end());
 
                 computePredecessors();
@@ -126,7 +125,7 @@ namespace storm {
                 // default comparison on pair actually works fine if distance is the first entry
                 std::set<std::pair<T, state_t>, std::greater<std::pair<T, state_t>>> dijkstraQueue;
 
-                for (state_t initialState : model->getInitialStates()) {
+                for (state_t initialState : initialStates) {
                     shortestPathDistances[initialState] = zeroDistance;
                     dijkstraQueue.emplace(zeroDistance, initialState);
                 }
@@ -179,7 +178,7 @@ namespace storm {
 
                 // BFS in Dijkstra-SP order
                 std::queue<state_t> bfsQueue;
-                for (state_t initialState : model->getInitialStates()) {
+                for (state_t initialState : initialStates) {
                     bfsQueue.push(initialState);
                 }
 
diff --git a/src/utility/shortestPaths.h b/src/utility/shortestPaths.h
index 8139f1c91..64fa16ca6 100644
--- a/src/utility/shortestPaths.h
+++ b/src/utility/shortestPaths.h
@@ -63,7 +63,13 @@ namespace storm {
                 // all of which will be converted to list and delegated to constructor above
                 ShortestPathsGenerator(std::shared_ptr<models::sparse::Model<T>> model, state_t singleTarget);
                 ShortestPathsGenerator(std::shared_ptr<models::sparse::Model<T>> model, storage::BitVector const& targetBV);
-                ShortestPathsGenerator(std::shared_ptr<models::sparse::Model<T>> model, std::string const& targetLabel);
+                ShortestPathsGenerator(std::shared_ptr<models::sparse::Model<T>> model, std::string const& targetLabel = "target");
+
+                // a further alternative: use transition matrix of maybe-states
+                // combined with target vector (e.g., the instantiated matrix/
+                // vector from SamplingModel);
+                // in this case separately specifying a target makes no sense
+                //ShortestPathsGenerator(storm::storage::SparseMatrix<T> maybeTransitionMatrix, std::vector<T> targetProbVector);
 
                 inline ~ShortestPathsGenerator(){}
 
@@ -91,13 +97,12 @@ namespace storm {
 
 
             private:
-                std::shared_ptr<models::sparse::Model<T>> model;
                 storage::SparseMatrix<T> transitionMatrix;
                 state_t numStates; // includes meta-target, i.e. states in model + 1
-
-                state_list_t targets;
                 std::unordered_set<state_t> targetSet;
                 state_t metaTarget;
+                storage::BitVector initialStates;
+                state_list_t targets;
 
                 std::vector<state_list_t>             graphPredecessors;
                 std::vector<boost::optional<state_t>> shortestPathPredecessors;
@@ -160,7 +165,6 @@ namespace storm {
 
                 // --- tiny helper fcts ---
                 inline bool isInitialState(state_t node) const {
-                    auto initialStates = model->getInitialStates();
                     return find(initialStates.begin(), initialStates.end(), node) != initialStates.end();
                 }