diff --git a/ChangeLog b/ChangeLog
index 8c0dbb134..2af6cf246 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -63,6 +63,8 @@ Changes
      Alex Hixon.
    * Allow configuring the shared library extension by setting the DLEXT
      environment variable when using the project makefiles.
+   * Optimize unnecessary zeroing in mbedtls_mpi_copy. Based on a contribution
+     by Alexey Skalozub in #405.
 
 = mbed TLS 2.8.0 branch released 2018-03-16
 
diff --git a/include/mbedtls/bignum.h b/include/mbedtls/bignum.h
index 3bf02a7ee..31383b1eb 100644
--- a/include/mbedtls/bignum.h
+++ b/include/mbedtls/bignum.h
@@ -204,6 +204,8 @@ void mbedtls_mpi_free( mbedtls_mpi *X );
 /**
  * \brief          Enlarge to the specified number of limbs
  *
+ *                 This function does nothing if the MPI is already large enough.
+ *
  * \param X        MPI to grow
  * \param nblimbs  The target number of limbs
  *
@@ -215,19 +217,23 @@ int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
 /**
  * \brief          Resize down, keeping at least the specified number of limbs
  *
+ *                 If \c X is smaller than \c nblimbs, it is resized up
+ *                 instead.
+ *
  * \param X        MPI to shrink
  * \param nblimbs  The minimum number of limbs to keep
  *
  * \return         0 if successful,
  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ *                 (this can only happen when resizing up).
  */
 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
 
 /**
  * \brief          Copy the contents of Y into X
  *
- * \param X        Destination MPI
- * \param Y        Source MPI
+ * \param X        Destination MPI. It is enlarged if necessary.
+ * \param Y        Source MPI.
  *
  * \return         0 if successful,
  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
diff --git a/library/bignum.c b/library/bignum.c
index ff72d30d0..47bf1ef97 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -184,7 +184,7 @@ int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs )
  */
 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y )
 {
-    int ret;
+    int ret = 0;
     size_t i;
 
     if( X == Y )
@@ -203,9 +203,15 @@ int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y )
 
     X->s = Y->s;
 
-    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i ) );
+    if( X->n < i )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i ) );
+    }
+    else
+    {
+        memset( X->p + i, 0, ( X->n - i ) * ciL );
+    }
 
-    memset( X->p, 0, X->n * ciL );
     memcpy( X->p, Y->p, i * ciL );
 
 cleanup: