diff --git a/Eigen/src/Cholesky/LLT.h b/Eigen/src/Cholesky/LLT.h
index a1706e53e..ad737aaeb 100644
--- a/Eigen/src/Cholesky/LLT.h
+++ b/Eigen/src/Cholesky/LLT.h
@@ -224,18 +224,18 @@ template<> struct ei_llt_inplace<UpperTriangular>
 template<typename MatrixType> struct LLT_Traits<MatrixType,LowerTriangular>
 {
   typedef TriangularView<MatrixType, LowerTriangular> MatrixL;
-  typedef TriangularView<NestByValue<typename MatrixType::AdjointReturnType>, UpperTriangular> MatrixU;
+  typedef TriangularView<typename MatrixType::AdjointReturnType, UpperTriangular> MatrixU;
   inline static MatrixL getL(const MatrixType& m) { return m; }
-  inline static MatrixU getU(const MatrixType& m) { return m.adjoint().nestByValue(); }
+  inline static MatrixU getU(const MatrixType& m) { return m.adjoint(); }
   static bool inplace_decomposition(MatrixType& m)
   { return ei_llt_inplace<LowerTriangular>::blocked(m); }
 };
 
 template<typename MatrixType> struct LLT_Traits<MatrixType,UpperTriangular>
 {
-  typedef TriangularView<NestByValue<typename MatrixType::AdjointReturnType>, LowerTriangular> MatrixL;
+  typedef TriangularView<typename MatrixType::AdjointReturnType, LowerTriangular> MatrixL;
   typedef TriangularView<MatrixType, UpperTriangular> MatrixU;
-  inline static MatrixL getL(const MatrixType& m) { return m.adjoint().nestByValue(); }
+  inline static MatrixL getL(const MatrixType& m) { return m.adjoint(); }
   inline static MatrixU getU(const MatrixType& m) { return m; }
   static bool inplace_decomposition(MatrixType& m)
   { return ei_llt_inplace<UpperTriangular>::blocked(m); }
diff --git a/Eigen/src/Eigenvalues/HessenbergDecomposition.h b/Eigen/src/Eigenvalues/HessenbergDecomposition.h
index cce76b288..9f7df49bc 100644
--- a/Eigen/src/Eigenvalues/HessenbergDecomposition.h
+++ b/Eigen/src/Eigenvalues/HessenbergDecomposition.h
@@ -58,10 +58,10 @@ template<typename _MatrixType> class HessenbergDecomposition
     typedef Matrix<RealScalar, Size, 1> DiagonalType;
     typedef Matrix<RealScalar, SizeMinusOne, 1> SubDiagonalType;
 
-    typedef typename NestByValue<Diagonal<MatrixType,0> >::RealReturnType DiagonalReturnType;
+    typedef typename Diagonal<MatrixType,0>::RealReturnType DiagonalReturnType;
 
-    typedef typename NestByValue<Diagonal<
-        NestByValue<Block<MatrixType,SizeMinusOne,SizeMinusOne> >,0 > >::RealReturnType SubDiagonalReturnType;
+    typedef typename Diagonal<
+        Block<MatrixType,SizeMinusOne,SizeMinusOne>,0 >::RealReturnType SubDiagonalReturnType;
 
     /** This constructor initializes a HessenbergDecomposition object for
       * further use with HessenbergDecomposition::compute()
diff --git a/Eigen/src/Eigenvalues/Tridiagonalization.h b/Eigen/src/Eigenvalues/Tridiagonalization.h
index 04b9f72d7..d8dcfb047 100644
--- a/Eigen/src/Eigenvalues/Tridiagonalization.h
+++ b/Eigen/src/Eigenvalues/Tridiagonalization.h
@@ -61,15 +61,15 @@ template<typename _MatrixType> class Tridiagonalization
     typedef Matrix<RealScalar, SizeMinusOne, 1> SubDiagonalType;
 
     typedef typename ei_meta_if<NumTraits<Scalar>::IsComplex,
-              typename NestByValue<Diagonal<MatrixType,0> >::RealReturnType,
+              typename Diagonal<MatrixType,0>::RealReturnType,
               Diagonal<MatrixType,0>
             >::ret DiagonalReturnType;
 
     typedef typename ei_meta_if<NumTraits<Scalar>::IsComplex,
-              typename NestByValue<Diagonal<
-                NestByValue<Block<MatrixType,SizeMinusOne,SizeMinusOne> >,0 > >::RealReturnType,
+              typename Diagonal<
+                Block<MatrixType,SizeMinusOne,SizeMinusOne>,0 >::RealReturnType,
               Diagonal<
-                NestByValue<Block<MatrixType,SizeMinusOne,SizeMinusOne> >,0 >
+                Block<MatrixType,SizeMinusOne,SizeMinusOne>,0 >
             >::ret SubDiagonalReturnType;
 
     /** This constructor initializes a Tridiagonalization object for
@@ -144,7 +144,7 @@ template<typename MatrixType>
 const typename Tridiagonalization<MatrixType>::DiagonalReturnType
 Tridiagonalization<MatrixType>::diagonal(void) const
 {
-  return m_matrix.diagonal().nestByValue();
+  return m_matrix.diagonal();
 }
 
 /** \returns an expression of the sub-diagonal vector */
@@ -153,8 +153,7 @@ const typename Tridiagonalization<MatrixType>::SubDiagonalReturnType
 Tridiagonalization<MatrixType>::subDiagonal(void) const
 {
   int n = m_matrix.rows();
-  return Block<MatrixType,SizeMinusOne,SizeMinusOne>(m_matrix, 1, 0, n-1,n-1)
-    .nestByValue().diagonal().nestByValue();
+  return Block<MatrixType,SizeMinusOne,SizeMinusOne>(m_matrix, 1, 0, n-1,n-1).diagonal();
 }
 
 /** constructs and returns the tridiagonal matrix T.
diff --git a/Eigen/src/LU/FullPivLU.h b/Eigen/src/LU/FullPivLU.h
index 28dc0cd47..8d18e65f7 100644
--- a/Eigen/src/LU/FullPivLU.h
+++ b/Eigen/src/LU/FullPivLU.h
@@ -351,11 +351,11 @@ template<typename _MatrixType> class FullPivLU
       *
       * \sa MatrixBase::inverse()
       */
-    inline const ei_solve_retval<FullPivLU,NestByValue<typename MatrixType::IdentityReturnType> > inverse() const
+    inline const ei_solve_retval<FullPivLU,typename MatrixType::IdentityReturnType> inverse() const
     {
       ei_assert(m_isInitialized && "LU is not initialized.");
       ei_assert(m_lu.rows() == m_lu.cols() && "You can't take the inverse of a non-square matrix!");
-      return ei_solve_retval<FullPivLU,NestByValue<typename MatrixType::IdentityReturnType> >
+      return ei_solve_retval<FullPivLU,typename MatrixType::IdentityReturnType>
                (*this, MatrixType::Identity(m_lu.rows(), m_lu.cols()).nestByValue());
     }
 
diff --git a/Eigen/src/LU/PartialPivLU.h b/Eigen/src/LU/PartialPivLU.h
index 975f79287..84bc165df 100644
--- a/Eigen/src/LU/PartialPivLU.h
+++ b/Eigen/src/LU/PartialPivLU.h
@@ -143,10 +143,10 @@ template<typename _MatrixType> class PartialPivLU
       *
       * \sa MatrixBase::inverse(), LU::inverse()
       */
-    inline const ei_solve_retval<PartialPivLU,NestByValue<typename MatrixType::IdentityReturnType> > inverse() const
+    inline const ei_solve_retval<PartialPivLU,typename MatrixType::IdentityReturnType> inverse() const
     {
       ei_assert(m_isInitialized && "PartialPivLU is not initialized.");
-      return ei_solve_retval<PartialPivLU,NestByValue<typename MatrixType::IdentityReturnType> >
+      return ei_solve_retval<PartialPivLU,typename MatrixType::IdentityReturnType>
                (*this, MatrixType::Identity(m_lu.rows(), m_lu.cols()).nestByValue());
     }
 
diff --git a/Eigen/src/QR/ColPivHouseholderQR.h b/Eigen/src/QR/ColPivHouseholderQR.h
index e59ecac66..614aa0295 100644
--- a/Eigen/src/QR/ColPivHouseholderQR.h
+++ b/Eigen/src/QR/ColPivHouseholderQR.h
@@ -214,11 +214,11 @@ template<typename _MatrixType> class ColPivHouseholderQR
       *       Use isInvertible() to first determine whether this matrix is invertible.
       */
     inline const
-    ei_solve_retval<ColPivHouseholderQR, NestByValue<typename MatrixType::IdentityReturnType> >
+    ei_solve_retval<ColPivHouseholderQR, typename MatrixType::IdentityReturnType>
     inverse() const
     {
       ei_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
-      return ei_solve_retval<ColPivHouseholderQR,NestByValue<typename MatrixType::IdentityReturnType> >
+      return ei_solve_retval<ColPivHouseholderQR,typename MatrixType::IdentityReturnType>
                (*this, MatrixType::Identity(m_qr.rows(), m_qr.cols()).nestByValue());
     }
 
diff --git a/Eigen/src/QR/FullPivHouseholderQR.h b/Eigen/src/QR/FullPivHouseholderQR.h
index ac0108046..db57ba088 100644
--- a/Eigen/src/QR/FullPivHouseholderQR.h
+++ b/Eigen/src/QR/FullPivHouseholderQR.h
@@ -216,11 +216,11 @@ template<typename _MatrixType> class FullPivHouseholderQR
       * \note If this matrix is not invertible, the returned matrix has undefined coefficients.
       *       Use isInvertible() to first determine whether this matrix is invertible.
       */    inline const
-    ei_solve_retval<FullPivHouseholderQR, NestByValue<typename MatrixType::IdentityReturnType> >
+    ei_solve_retval<FullPivHouseholderQR, typename MatrixType::IdentityReturnType>
     inverse() const
     {
       ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
-      return ei_solve_retval<FullPivHouseholderQR,NestByValue<typename MatrixType::IdentityReturnType> >
+      return ei_solve_retval<FullPivHouseholderQR,typename MatrixType::IdentityReturnType>
                (*this, MatrixType::Identity(m_qr.rows(), m_qr.cols()).nestByValue());
     }