diff --git a/Eigen/src/Core/util/Constants.h b/Eigen/src/Core/util/Constants.h
index 7908bf3b3..edfad7c55 100644
--- a/Eigen/src/Core/util/Constants.h
+++ b/Eigen/src/Core/util/Constants.h
@@ -357,7 +357,11 @@ enum NaNPropagationOptions {
  * and we do not know how to get rid of them (bug 450).
  */
 
-enum NoChange_t { NoChange };
+// NoChange is set to -1 (rather than 0) so that calls like resize(NoChange, n)
+// that land in a generic resize(Index, Index) overload — missing the NoChange_t
+// overload — trip the rows/cols >= 0 assertion instead of silently producing a
+// 0-sized dimension. See issue #656.
+enum NoChange_t { NoChange = -1 };
 enum Sequential_t { Sequential };
 enum Default_t { Default };
 
diff --git a/Eigen/src/SparseCore/SparseMatrix.h b/Eigen/src/SparseCore/SparseMatrix.h
index b85d1ad0d..8c97a11be 100644
--- a/Eigen/src/SparseCore/SparseMatrix.h
+++ b/Eigen/src/SparseCore/SparseMatrix.h
@@ -725,6 +725,12 @@ class SparseMatrix : public SparseCompressedBase<SparseMatrix<Scalar_, Options_,
     m_data.resize(newSize);
   }
 
+  /** \sa conservativeResize(Index,Index) */
+  void conservativeResize(NoChange_t, Index cols) { conservativeResize(rows(), cols); }
+
+  /** \sa conservativeResize(Index,Index) */
+  void conservativeResize(Index rows, NoChange_t) { conservativeResize(rows, cols()); }
+
   /** Resizes the matrix to a \a rows x \a cols matrix and initializes it to zero.
    *
    * This function does not free the currently allocated memory. To release as much as memory as possible,
@@ -750,6 +756,12 @@ class SparseMatrix : public SparseCompressedBase<SparseMatrix<Scalar_, Options_,
     fill_n(m_outerIndex, m_outerSize + 1, StorageIndex(0));
   }
 
+  /** \sa resize(Index,Index) */
+  void resize(NoChange_t, Index cols) { resize(rows(), cols); }
+
+  /** \sa resize(Index,Index) */
+  void resize(Index rows, NoChange_t) { resize(rows, cols()); }
+
   /** \internal
    * Resize the nonzero vector to \a size */
   void resizeNonZeros(Index size) { m_data.resize(size); }
diff --git a/Eigen/src/SparseCore/SparseVector.h b/Eigen/src/SparseCore/SparseVector.h
index 7dc94d30b..d60943ba9 100644
--- a/Eigen/src/SparseCore/SparseVector.h
+++ b/Eigen/src/SparseCore/SparseVector.h
@@ -228,6 +228,12 @@ class SparseVector : public SparseCompressedBase<SparseVector<Scalar_, Options_,
     resize(IsColVector ? rows : cols);
   }
 
+  /** \sa resize(Index,Index) */
+  void resize(NoChange_t, Index cols) { resize(rows(), cols); }
+
+  /** \sa resize(Index,Index) */
+  void resize(Index rows, NoChange_t) { resize(rows, cols()); }
+
   /** Resizes the sparse vector to \a newSize
    * This method deletes all entries, thus leaving an empty sparse vector
    *
diff --git a/test/sparse_basic.cpp b/test/sparse_basic.cpp
index f3f0a1878..087604b8b 100644
--- a/test/sparse_basic.cpp
+++ b/test/sparse_basic.cpp
@@ -935,6 +935,38 @@ void sparse_basic(const SparseMatrixType& ref) {
     }
   }
 
+  // test resize / conservativeResize with Eigen::NoChange (bug #656)
+  {
+    SparseMatrixType m1(rows, cols);
+    DenseMatrix refMat1 = DenseMatrix::Zero(rows, cols);
+    initSparse<Scalar>(density, refMat1, m1);
+
+    SparseMatrixType m2 = m1;
+
+    m1.conservativeResize(NoChange, cols + 2);
+    refMat1.conservativeResize(NoChange, cols + 2);
+    refMat1.rightCols(2).setZero();
+    VERIFY_IS_APPROX(m1, refMat1);
+
+    m1.conservativeResize(rows + 1, NoChange);
+    refMat1.conservativeResize(rows + 1, NoChange);
+    refMat1.bottomRows(1).setZero();
+    VERIFY_IS_APPROX(m1, refMat1);
+
+    m2.resize(NoChange, cols + 4);
+    VERIFY(m2.rows() == rows && m2.cols() == cols + 4);
+    VERIFY(m2.nonZeros() == 0);
+
+    m2.resize(rows + 2, NoChange);
+    VERIFY(m2.rows() == rows + 2 && m2.cols() == cols + 4);
+
+    SparseVector<Scalar, ColMajor, StorageIndex> v(rows);
+    v.resize(NoChange, 1);
+    VERIFY(v.size() == rows);
+    v.resize(rows + 3, NoChange);
+    VERIFY(v.size() == rows + 3);
+  }
+
   // test Identity matrix
   {
     DenseMatrix refMat1 = DenseMatrix::Identity(rows, rows);