diff --git a/library/ecp.c b/library/ecp.c
index 2168981afb..d3c6ccc8de 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -1738,18 +1738,17 @@ static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *p
     /* Generate l such that 1 < l < p */
     do
     {
-        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
-
-        while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
-            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
-
-        if( count++ > 10 )
+        if( count++ > 30 )
         {
             ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
             goto cleanup;
         }
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, ( p_size * 8 ) - grp->pbits ) );
     }
-    while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
+    while( ( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 ) ||
+           ( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 ) );
 
     /* Z = l * Z */
     MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z,   &pt->Z,     &l  ) ); MOD_MUL( pt->Z );
@@ -2514,18 +2513,17 @@ static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P
     /* Generate l such that 1 < l < p */
     do
     {
-        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
-
-        while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
-            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
-
-        if( count++ > 10 )
+        if( count++ > 30 )
         {
             ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
             goto cleanup;
         }
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, ( p_size * 8 ) - grp->pbits ) );
     }
-    while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
+    while( ( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 ) ||
+           ( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 ) );
 
     MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
     MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );