diff --git a/library/ecp.c b/library/ecp.c
index b1c4548..a27d30e 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -1796,7 +1796,16 @@
             MPI_CHK( mpi_read_binary( d, rnd, n_size ) );
             MPI_CHK( mpi_shift_r( d, 8 * n_size - grp->nbits ) );
 
-            if( count++ > 10 )
+            /*
+             * Each try has at worst a probability 1/2 of failing (the msb has
+             * a probability 1/2 of being 0, and then the result will be < N),
+             * so after 30 tries failure probability is a most 2**(-30).
+             *
+             * For most curves, 1 try is enough with overwhelming probability,
+             * since N starts with a lot of 1s in binary, but some curves
+             * such as secp224k1 are actually very close to the worst case.
+             */
+            if( ++count > 30 )
                 return( POLARSSL_ERR_ECP_RANDOM_FAILED );
         }
         while( mpi_cmp_int( d, 1 ) < 0 ||