diff --git a/Eigen/src/SparseCore/SparseMatrix.h b/Eigen/src/SparseCore/SparseMatrix.h
index b27061f9e..272f1d7b4 100644
--- a/Eigen/src/SparseCore/SparseMatrix.h
+++ b/Eigen/src/SparseCore/SparseMatrix.h
@@ -729,7 +729,8 @@ class SparseMatrix
       m_data.swap(other.m_data);
     }
 
-    /** Sets *this to the identity matrix */
+    /** Sets *this to the identity matrix.
+      * This function also turns the matrix into compressed mode, and drop any reserved memory. */
     inline void setIdentity()
     {
       eigen_assert(rows() == cols() && "ONLY FOR SQUARED MATRICES");
@@ -737,6 +738,8 @@ class SparseMatrix
       Eigen::Map<IndexVector>(&this->m_data.index(0), rows()).setLinSpaced(0, StorageIndex(rows()-1));
       Eigen::Map<ScalarVector>(&this->m_data.value(0), rows()).setOnes();
       Eigen::Map<IndexVector>(this->m_outerIndex, rows()+1).setLinSpaced(0, StorageIndex(rows()));
+      std::free(m_innerNonZeros);
+      m_innerNonZeros = 0;
     }
     inline SparseMatrix& operator=(const SparseMatrix& other)
     {
diff --git a/test/sparse_basic.cpp b/test/sparse_basic.cpp
index 993f7840c..e8ebd7000 100644
--- a/test/sparse_basic.cpp
+++ b/test/sparse_basic.cpp
@@ -434,6 +434,20 @@ template<typename SparseMatrixType> void sparse_basic(const SparseMatrixType& re
     SparseMatrixType m1(rows, rows);
     m1.setIdentity();
     VERIFY_IS_APPROX(m1, refMat1);
+    for(int k=0; k<rows*rows/4; ++k)
+    {
+      Index i = internal::random<Index>(0,rows-1);
+      Index j = internal::random<Index>(0,rows-1);
+      Index v = internal::random<Scalar>();
+      m1.coeffRef(i,j) = v;
+      refMat1.coeffRef(i,j) = v;
+      VERIFY_IS_APPROX(m1, refMat1);
+      if(internal::random<Index>(0,10)<2)
+        m1.makeCompressed();
+    }
+    m1.setIdentity();
+    refMat1.setIdentity();
+    VERIFY_IS_APPROX(m1, refMat1);
   }
 }