diff --git a/crypto/bn/bn.h b/crypto/bn/bn.h
index da2a0e182..47d8c71d9 100644
--- a/crypto/bn/bn.h
+++ b/crypto/bn/bn.h
@@ -934,6 +934,7 @@ void ERR_load_BN_strings(void);
 # define BN_R_ARG2_LT_ARG3                                100
 # define BN_R_BAD_RECIPROCAL                              101
 # define BN_R_BIGNUM_TOO_LONG                             114
+# define BN_R_BITS_TOO_SMALL                              118
 # define BN_R_CALLED_WITH_EVEN_MODULUS                    102
 # define BN_R_DIV_BY_ZERO                                 103
 # define BN_R_ENCODING_ERROR                              104
diff --git a/crypto/bn/bn_err.c b/crypto/bn/bn_err.c
index a9b7f5193..e7a703826 100644
--- a/crypto/bn/bn_err.c
+++ b/crypto/bn/bn_err.c
@@ -1,6 +1,6 @@
 /* crypto/bn/bn_err.c */
 /* ====================================================================
- * Copyright (c) 1999-2007 The OpenSSL Project.  All rights reserved.
+ * Copyright (c) 1999-2015 The OpenSSL Project.  All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions
@@ -119,6 +119,7 @@ static ERR_STRING_DATA BN_str_reasons[] = {
     {ERR_REASON(BN_R_ARG2_LT_ARG3), "arg2 lt arg3"},
     {ERR_REASON(BN_R_BAD_RECIPROCAL), "bad reciprocal"},
     {ERR_REASON(BN_R_BIGNUM_TOO_LONG), "bignum too long"},
+    {ERR_REASON(BN_R_BITS_TOO_SMALL), "bits too small"},
     {ERR_REASON(BN_R_CALLED_WITH_EVEN_MODULUS), "called with even modulus"},
     {ERR_REASON(BN_R_DIV_BY_ZERO), "div by zero"},
     {ERR_REASON(BN_R_ENCODING_ERROR), "encoding error"},
diff --git a/crypto/bn/bn_rand.c b/crypto/bn/bn_rand.c
index 9e78d4d42..f9fb2e9e4 100644
--- a/crypto/bn/bn_rand.c
+++ b/crypto/bn/bn_rand.c
@@ -121,6 +121,11 @@ static int bnrand(int pseudorand, BIGNUM *rnd, int bits, int top, int bottom)
     int ret = 0, bit, bytes, mask;
     time_t tim;
 
+    if (bits < 0 || (bits == 1 && top > 0)) {
+        BNerr(BN_F_BNRAND, BN_R_BITS_TOO_SMALL);
+        return 0;
+    }
+
     if (bits == 0) {
         BN_zero(rnd);
         return 1;
@@ -169,7 +174,7 @@ static int bnrand(int pseudorand, BIGNUM *rnd, int bits, int top, int bottom)
     }
 #endif
 
-    if (top != -1) {
+    if (top >= 0) {
         if (top) {
             if (bit == 0) {
                 buf[0] = 1;
diff --git a/doc/crypto/BN_rand.pod b/doc/crypto/BN_rand.pod
index 81f93c2eb..3b2796c5d 100644
--- a/doc/crypto/BN_rand.pod
+++ b/doc/crypto/BN_rand.pod
@@ -24,7 +24,8 @@ most significant bit of the random number can be zero. If B<top> is 0,
 it is set to 1, and if B<top> is 1, the two most significant bits of
 the number will be set to 1, so that the product of two such random
 numbers will always have 2*B<bits> length.  If B<bottom> is true, the
-number will be odd.
+number will be odd. The value of B<bits> must be zero or greater. If B<bits> is
+1 then B<top> cannot also be 1.
 
 BN_pseudo_rand() does the same, but pseudo-random numbers generated by
 this function are not necessarily unpredictable. They can be used for