diff --git a/include/mxx/reduction.hpp b/include/mxx/reduction.hpp
index 24bac16..7fb7bb5 100644
--- a/include/mxx/reduction.hpp
+++ b/include/mxx/reduction.hpp
@@ -174,9 +174,8 @@ struct get_builtin_op<T, const T&(*) (const T&, const T&)> {
  * @note    This assumes that the operator is commutative.
  *
  * @tparam T    The input and ouput datatype of the binary operator.
- * @tparam IsCommutative    Whether or not the operation is commutative (default = true).
  */
-template <typename T, bool IsCommutative = true>
+template <typename T>
 class custom_op {
 public:
 
@@ -184,13 +183,14 @@ class custom_op {
      * @brief Creates a custom operator given a functor and the associated
      *        `MPI_Datatype`.
      *
-     * @tparam Func     Type of the functor, can be a function pointer, lambda
-     *                  function, or std::function or any object with a
-     *                  `T operator(T& x, T& y)` member.
-     * @param func      The instance of the functor.
+     * @tparam Func        Type of the functor, can be a function pointer, lambda
+     *                     function, or std::function or any object with a
+     *                     `T operator(T& x, T& y)` member.
+     * @param func         The instance of the functor.
+     * @param commutative  Whether or not the operation is commutative (default = true).
      */
     template <typename Func>
-    custom_op(Func func) : m_builtin(false) {
+    custom_op(Func func, const bool commutative = true) : m_builtin(false) {
         if (mxx::is_builtin_type<T>::value) {
             // check if the operator is MPI built-in (in case the type
             // is also a MPI built-in type)
@@ -215,7 +215,7 @@ class custom_op {
             MPI_Type_dup(dt.type(), &m_type_copy);
             attr_map<int, func_t>::set(m_type_copy, 1347, m_user_func);
             // create op
-            MPI_Op_create(&custom_op::mpi_user_function, IsCommutative, &m_op);
+            MPI_Op_create(&custom_op::mpi_user_function, commutative, &m_op);
         }
     }
 
@@ -731,7 +731,7 @@ inline std::vector<T> local_scan(const std::vector<T>& in) {
 // global scans
 
 template <typename InIterator, typename OutIterator, typename Func>
-void global_scan(InIterator begin, InIterator end, OutIterator out, Func func, const mxx::comm& comm = mxx::comm()) {
+void global_scan(InIterator begin, InIterator end, OutIterator out, Func func, const mxx::comm& comm = mxx::comm(), const bool commutative = true) {
     OutIterator o = out;
     size_t n = std::distance(begin, end);
     // create subcommunicator for those processes which contain elements
@@ -744,7 +744,7 @@ void global_scan(InIterator begin, InIterator end, OutIterator out, Func func, c
         T sum = T();
         if (n > 0)
             sum = *(out+(n-1));
-        T presum = exscan(sum, func, nonzero_comm);
+        T presum = exscan(sum, func, nonzero_comm, commutative);
         // accumulate previous sum on all local elements
         for (size_t i = 0; i < n; ++i) {
             *o = func(presum, *o);
@@ -756,7 +756,7 @@ void global_scan(InIterator begin, InIterator end, OutIterator out, Func func, c
 
 // inplace!
 template <typename Iterator, typename Func>
-inline void global_scan_inplace(Iterator begin, Iterator end, Func func, const mxx::comm& comm = mxx::comm()) {
+inline void global_scan_inplace(Iterator begin, Iterator end, Func func, const mxx::comm& comm = mxx::comm(), const bool commutative = true) {
     Iterator o = begin;
     size_t n = std::distance(begin, end);
     mxx::comm nonzero_comm = comm.split(n > 0);
@@ -766,7 +766,7 @@ inline void global_scan_inplace(Iterator begin, Iterator end, Func func, const m
         // mxx::exscan
         typedef typename std::iterator_traits<Iterator>::value_type T;
         T sum = *(begin + (n-1));
-        T presum = exscan(sum, func, nonzero_comm);
+        T presum = exscan(sum, func, nonzero_comm, commutative);
 
         // accumulate previous sum on all local elements
         for (size_t i = 0; i < n; ++i) {
@@ -788,8 +788,8 @@ inline void global_scan_inplace(Iterator begin, Iterator end, const mxx::comm& c
 
 // std::vector overloads
 template <typename T, typename Func>
-inline void global_scan_inplace(std::vector<T>& in, Func func, const mxx::comm& comm = mxx::comm()) {
-    global_scan_inplace(in.begin(), in.end(), func, comm);
+inline void global_scan_inplace(std::vector<T>& in, Func func, const mxx::comm& comm = mxx::comm(), const bool commutative = true) {
+    global_scan_inplace(in.begin(), in.end(), func, comm, commutative);
 }
 
 template <typename T>
@@ -798,9 +798,9 @@ inline void global_scan_inplace(std::vector<T>& in, const mxx::comm& comm = mxx:
 }
 
 template <typename T, typename Func>
-inline std::vector<T> global_scan(const std::vector<T>& in, Func func, const mxx::comm& comm = mxx::comm()) {
+inline std::vector<T> global_scan(const std::vector<T>& in, Func func, const mxx::comm& comm = mxx::comm(), const bool commutative = true) {
     std::vector<T> result(in.size());
-    global_scan(in.begin(), in.end(), result.begin(), func, comm);
+    global_scan(in.begin(), in.end(), result.begin(), func, comm, commutative);
     return result;
 }
 
@@ -838,9 +838,9 @@ inline std::vector<T> exscan_vec(const std::vector<T>& x, Func func, const mxx::
 // single element
 
 template <typename T, typename Func>
-T exscan(const T& x, Func func, const mxx::comm& comm = mxx::comm()) {
+T exscan(const T& x, Func func, const mxx::comm& comm = mxx::comm(), const bool commutative = true) {
     // get op
-    mxx::custom_op<T> op(std::forward<Func>(func));
+    mxx::custom_op<T> op(std::forward<Func>(func), commutative);
     // perform reduction
     T result;
     MPI_Exscan(const_cast<T*>(&x), &result, 1, op.get_type(), op.get_op(), comm);