diff --git a/test/nullary.cpp b/test/nullary.cpp
index d46349991..9f08ec23a 100644
--- a/test/nullary.cpp
+++ b/test/nullary.cpp
@@ -49,11 +49,12 @@ bool equalsIdentity(const MatrixType& A)
 template<typename VectorType>
 void testVectorType(const VectorType& base)
 {
+  typedef typename ei_traits<VectorType>::Index Index;
   typedef typename ei_traits<VectorType>::Scalar Scalar;
   Scalar low = ei_random<Scalar>(-500,500);
   Scalar high = ei_random<Scalar>(-500,500);
   if (low>high) std::swap(low,high);
-  const int size = base.size();
+  const Index size = base.size();
   const Scalar step = (high-low)/(size-1);
 
   // check whether the result yields what we expect it to do
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
index 299809205..006371474 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
@@ -132,7 +132,7 @@ class MatrixExponential {
     typedef typename NumTraits<Scalar>::Real RealScalar;
 
     /** \brief Reference to matrix whose exponential is to be computed. */
-    const typename ei_nested<MatrixType>::type m_M;
+    typename ei_nested<MatrixType>::type m_M;
 
     /** \brief Even-degree terms in numerator of Pad&eacute; approximant. */
     MatrixType m_U;
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
index 17040c5f3..ae5dcab59 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
@@ -117,7 +117,7 @@ class MatrixFunction<MatrixType, 0>
     }
 
   private:
-    const typename ei_nested<MatrixType>::type m_A; /**< \brief Reference to argument of matrix function. */
+    typename ei_nested<MatrixType>::type m_A; /**< \brief Reference to argument of matrix function. */
     StemFunction *m_f; /**< \brief Stem function for matrix function under consideration */    
 
     MatrixFunction& operator=(const MatrixFunction&);
@@ -167,7 +167,7 @@ class MatrixFunction<MatrixType, 1>
     void computeOffDiagonal();
     DynMatrixType solveTriangularSylvester(const DynMatrixType& A, const DynMatrixType& B, const DynMatrixType& C);
 
-    const typename ei_nested<MatrixType>::type m_A; /**< \brief Reference to argument of matrix function. */
+    typename ei_nested<MatrixType>::type m_A; /**< \brief Reference to argument of matrix function. */
     StemFunction *m_f; /**< \brief Stem function for matrix function under consideration */
     MatrixType m_T; /**< \brief Triangular part of Schur decomposition */
     MatrixType m_U; /**< \brief Unitary part of Schur decomposition */
@@ -529,7 +529,7 @@ template<typename Derived> class MatrixFunctionReturnValue
     Index cols() const { return m_A.cols(); }
 
   private:
-    const typename ei_nested<Derived>::type m_A;
+    typename ei_nested<Derived>::type m_A;
     StemFunction *m_f;
 
     MatrixFunctionReturnValue& operator=(const MatrixFunctionReturnValue&);
diff --git a/unsupported/test/matrix_function.cpp b/unsupported/test/matrix_function.cpp
index 16995d836..3455fb936 100644
--- a/unsupported/test/matrix_function.cpp
+++ b/unsupported/test/matrix_function.cpp
@@ -38,12 +38,13 @@ inline bool test_isApprox_abs(const Type1& a, const Type2& b)
 
 // Returns a matrix with eigenvalues clustered around 0, 1 and 2.
 template<typename MatrixType>
-MatrixType randomMatrixWithRealEivals(const int size)
+MatrixType randomMatrixWithRealEivals(const typename MatrixType::Index size)
 {
+  typedef typename MatrixType::Index Index;
   typedef typename MatrixType::Scalar Scalar;
   typedef typename MatrixType::RealScalar RealScalar;
   MatrixType diag = MatrixType::Zero(size, size);
-  for (int i = 0; i < size; ++i) {
+  for (Index i = 0; i < size; ++i) {
     diag(i, i) = Scalar(RealScalar(ei_random<int>(0,2)))
       + ei_random<Scalar>() * Scalar(RealScalar(0.01));
   }
@@ -56,20 +57,21 @@ template <typename MatrixType, int IsComplex = NumTraits<typename ei_traits<Matr
 struct randomMatrixWithImagEivals
 {
   // Returns a matrix with eigenvalues clustered around 0 and +/- i.
-  static MatrixType run(const int size);
+  static MatrixType run(const typename MatrixType::Index size);
 };
 
 // Partial specialization for real matrices
 template<typename MatrixType>
 struct randomMatrixWithImagEivals<MatrixType, 0>
 {
-  static MatrixType run(const int size)
+  static MatrixType run(const typename MatrixType::Index size)
   {
+    typedef typename MatrixType::Index Index;
     typedef typename MatrixType::Scalar Scalar;
     MatrixType diag = MatrixType::Zero(size, size);
-    int i = 0;
+    Index i = 0;
     while (i < size) {
-      int randomInt = ei_random<int>(-1, 1);
+      Index randomInt = ei_random<Index>(-1, 1);
       if (randomInt == 0 || i == size-1) {
         diag(i, i) = ei_random<Scalar>() * Scalar(0.01);
         ++i;
@@ -90,14 +92,14 @@ struct randomMatrixWithImagEivals<MatrixType, 0>
 template<typename MatrixType>
 struct randomMatrixWithImagEivals<MatrixType, 1>
 {
-  static MatrixType run(const int size)
+  static MatrixType run(const typename MatrixType::Index size)
   {
     typedef typename MatrixType::Scalar Scalar;
     typedef typename MatrixType::RealScalar RealScalar;
     const Scalar imagUnit(0, 1);
     MatrixType diag = MatrixType::Zero(size, size);
-    for (int i = 0; i < size; ++i) {
-      diag(i, i) = Scalar(RealScalar(ei_random<int>(-1, 1))) * imagUnit
+    for (Index i = 0; i < size; ++i) {
+      diag(i, i) = Scalar(RealScalar(ei_random<Index>(-1, 1))) * imagUnit
         + ei_random<Scalar>() * Scalar(RealScalar(0.01));
     }
     MatrixType A = MatrixType::Random(size, size);
@@ -163,8 +165,9 @@ void testMatrixType(const MatrixType& m)
 {
   // Matrices with clustered eigenvalue lead to different code paths
   // in MatrixFunction.h and are thus useful for testing.
+  typedef typename MatrixType::Index Index;
 
-  const int size = m.rows();
+  const Index size = m.rows();
   for (int i = 0; i < g_repeat; i++) {
     testMatrix(MatrixType::Random(size, size).eval());
     testMatrix(randomMatrixWithRealEivals<MatrixType>(size));