diff --git a/unsupported/Eigen/IterativeSolvers b/unsupported/Eigen/IterativeSolvers
index 42f4a32f1..e690b0300 100644
--- a/unsupported/Eigen/IterativeSolvers
+++ b/unsupported/Eigen/IterativeSolvers
@@ -41,8 +41,11 @@ namespace Eigen {
   */
 //@{
 
+#include "../../Eigen/src/misc/Solve.h"
+
 #include "src/IterativeSolvers/IterationController.h"
 #include "src/IterativeSolvers/ConstrainedConjGrad.h"
+#include "src/IterativeSolvers/BasicPreconditioners.h"
 #include "src/IterativeSolvers/ConjugateGradient.h"
 
 //@}
diff --git a/unsupported/Eigen/src/IterativeSolvers/BasicPreconditioners.h b/unsupported/Eigen/src/IterativeSolvers/BasicPreconditioners.h
new file mode 100644
index 000000000..b016e5bf3
--- /dev/null
+++ b/unsupported/Eigen/src/IterativeSolvers/BasicPreconditioners.h
@@ -0,0 +1,139 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_BASIC_PRECONDITIONERS_H
+#define EIGEN_BASIC_PRECONDITIONERS_H
+
+/** \brief A preconditioner based on the digonal entries
+  *
+  * This class allows to approximately solve for A.x = b problems assuming A is a diagonal matrix.
+  * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
+  * \code
+  * A.diagonal().asDiagonal() . x = b
+  * \endcode
+  *
+  * \tparam _Scalar the type of the scalar.
+  *
+  * This preconditioner is suitable for both selfadjoint and general problems.
+  * The diagonal entries are pre-inverted and stored into a dense vector.
+  *
+  * \note A variant that has yet to be implemented would attempt to preserve the norm of each column.
+  *
+  */
+template <typename _Scalar>
+class DiagonalPreconditioner
+{
+    typedef _Scalar Scalar;
+    typedef Matrix<Scalar,Dynamic,1> Vector;
+    typedef typename Vector::Index Index;
+
+  public:
+    typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
+
+    DiagonalPreconditioner() : m_isInitialized(false) {}
+
+    template<typename MatrixType>
+    DiagonalPreconditioner(const MatrixType& mat) : m_invdiag(mat.cols())
+    {
+      compute(mat);
+    }
+
+    Index rows() const { return m_invdiag.size(); }
+    Index cols() const { return m_invdiag.size(); }
+
+    template<typename MatrixType>
+    DiagonalPreconditioner& compute(const MatrixType& mat)
+    {
+      m_invdiag.resize(mat.cols());
+      for(int j=0; j<mat.outerSize(); ++j)
+      {
+        typename MatrixType::InnerIterator it(mat,j);
+        while(it && it.index()!=j) ++it;
+        if(it.index()==j)
+          m_invdiag(j) = Scalar(1)/it.value();
+        else
+          m_invdiag(j) = 0;
+      }
+      m_isInitialized = true;
+      return *this;
+    }
+
+    template<typename Rhs, typename Dest>
+    void _solve(const Rhs& b, Dest& x) const
+    {
+      x = m_invdiag.array() * b.array() ;
+    }
+
+    template<typename Rhs> inline const internal::solve_retval<DiagonalPreconditioner, Rhs>
+    solve(const MatrixBase<Rhs>& b) const
+    {
+      eigen_assert(m_isInitialized && "DiagonalPreconditioner is not initialized.");
+      eigen_assert(m_invdiag.size()==b.rows()
+                && "DiagonalPreconditioner::solve(): invalid number of rows of the right hand side matrix b");
+      return internal::solve_retval<DiagonalPreconditioner, Rhs>(*this, b.derived());
+    }
+
+  protected:
+    Vector m_invdiag;
+    bool m_isInitialized;
+};
+
+namespace internal {
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<DiagonalPreconditioner<_MatrixType>, Rhs>
+  : solve_retval_base<DiagonalPreconditioner<_MatrixType>, Rhs>
+{
+  typedef DiagonalPreconditioner<_MatrixType> Dec;
+  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+  template<typename Dest> void evalTo(Dest& dst) const
+  {
+    dec()._solve(rhs(),dst);
+  }
+};
+
+}
+
+/** \brief A naive preconditioner which approximates any matrix as the identity matrix
+  *
+  * \sa class DiagonalPreconditioner
+  */
+class IdentityPreconditioner
+{
+  public:
+
+    IdentityPreconditioner() {}
+
+    template<typename MatrixType>
+    IdentityPreconditioner(const MatrixType& ) {}
+
+    template<typename MatrixType>
+    IdentityPreconditioner& compute(const MatrixType& ) { return *this; }
+    
+    template<typename Rhs>
+    inline const Rhs& solve(const Rhs& b) const { return b; }
+};
+
+#endif // EIGEN_BASIC_PRECONDITIONERS_H
diff --git a/unsupported/Eigen/src/IterativeSolvers/ConjugateGradient.h b/unsupported/Eigen/src/IterativeSolvers/ConjugateGradient.h
index 52d167b72..9054e55a7 100644
--- a/unsupported/Eigen/src/IterativeSolvers/ConjugateGradient.h
+++ b/unsupported/Eigen/src/IterativeSolvers/ConjugateGradient.h
@@ -83,95 +83,8 @@ void conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,
 
 }
 
-/** \brief A preconditioner based on the digonal entries
-  *
-  * This class allows to approximately solve for A.x = b problems assuming A is a diagonal matrix.
-  * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
-  * \code
-  * A.diagonal().asDiagonal() . x = b
-  * \endcode
-  *
-  * \tparam _Scalar the type of the scalar.
-  * 
-  * This preconditioner is suitable for both selfadjoint and general problems.
-  * The diagonal entries are pre-inverted and stored into a dense vector.
-  * 
-  * \note A variant that has yet to be implemented would attempt to preserve the norm of each column.
-  *
-  */
-template <typename _Scalar>
-class DiagonalPreconditioner
-{
-    typedef _Scalar Scalar;
-    typedef Matrix<Scalar,Dynamic,1> Vector;
-    typedef typename Vector::Index Index;
-
-  public:
-    typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
-    
-    DiagonalPreconditioner() : m_isInitialized(false) {}
-
-    template<typename MatrixType>
-    DiagonalPreconditioner(const MatrixType& mat) : m_invdiag(mat.cols())
-    {
-      compute(mat);
-    }
-
-    Index rows() const { return m_invdiag.size(); }
-    Index cols() const { return m_invdiag.size(); }
-
-    template<typename MatrixType>
-    DiagonalPreconditioner& compute(const MatrixType& mat)
-    {
-      m_invdiag.resize(mat.cols());
-      for(int j=0; j<mat.outerSize(); ++j)
-      {
-        typename MatrixType::InnerIterator it(mat,j);
-        while(it && it.index()!=j) ++it;
-        if(it.index()==j)
-          m_invdiag(j) = Scalar(1)/it.value();
-        else
-          m_invdiag(j) = 0;
-      }
-      m_isInitialized = true;
-      return *this;
-    }
-
-    template<typename Rhs, typename Dest>
-    void _solve(const Rhs& b, Dest& x) const
-    {
-      x = m_invdiag.array() * b.array() ;
-    }
-
-    template<typename Rhs> inline const internal::solve_retval<DiagonalPreconditioner, Rhs>
-    solve(const MatrixBase<Rhs>& b) const
-    {
-      eigen_assert(m_isInitialized && "DiagonalPreconditioner is not initialized.");
-      eigen_assert(m_invdiag.size()==b.rows()
-                && "DiagonalPreconditioner::solve(): invalid number of rows of the right hand side matrix b");
-      return internal::solve_retval<DiagonalPreconditioner, Rhs>(*this, b.derived());
-    }
-
-  protected:
-    Vector m_invdiag;
-    bool m_isInitialized;
-};
-
 namespace internal {
 
-template<typename _MatrixType, typename Rhs>
-struct solve_retval<DiagonalPreconditioner<_MatrixType>, Rhs>
-  : solve_retval_base<DiagonalPreconditioner<_MatrixType>, Rhs>
-{
-  typedef DiagonalPreconditioner<_MatrixType> Dec;
-  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
-
-  template<typename Dest> void evalTo(Dest& dst) const
-  {
-    dec()._solve(rhs(),dst);
-  }
-};
-
 template<typename CG, typename Rhs, typename Guess>
 class conjugate_gradient_solve_retval_with_guess;
 
diff --git a/unsupported/test/cg.cpp b/unsupported/test/cg.cpp
index aede84d58..bc421985e 100644
--- a/unsupported/test/cg.cpp
+++ b/unsupported/test/cg.cpp
@@ -57,10 +57,24 @@ template<typename Scalar,typename Index> void cg(int size)
   VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "ConjugateGradient: solve, full storage, upper, single dense rhs");
 
   x = ConjugateGradient<SparseMatrixType, Lower>(m3_lo).solve(b);
-  VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "SimplicialCholesky: solve, lower only, single dense rhs");
+  VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "ConjugateGradient: solve, lower only, single dense rhs");
 
   x = ConjugateGradient<SparseMatrixType, Upper>(m3_up).solve(b);
-  VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "SimplicialCholesky: solve, upper only, single dense rhs");
+  VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "ConjugateGradient: solve, upper only, single dense rhs");
+
+
+
+  x = ConjugateGradient<SparseMatrixType, Lower, IdentityPreconditioner>().compute(m3).solve(b);
+  VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "ConjugateGradient: solve, full storage, lower");
+
+  x = ConjugateGradient<SparseMatrixType, Upper, IdentityPreconditioner>().compute(m3).solve(b);
+  VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "ConjugateGradient: solve, full storage, upper, single dense rhs");
+
+  x = ConjugateGradient<SparseMatrixType, Lower, IdentityPreconditioner>(m3_lo).solve(b);
+  VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "ConjugateGradient: solve, lower only, single dense rhs");
+
+  x = ConjugateGradient<SparseMatrixType, Upper, IdentityPreconditioner>(m3_up).solve(b);
+  VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "ConjugateGradient: solve, upper only, single dense rhs");
 }
 
 void test_cg()