diff --git a/crypto/bn/bn_rand.c b/crypto/bn/bn_rand.c
index 4dd3f924a721321755181fb44971cceb6e6d161a..2764c8a30730e573c6c821d2c823ed00d5066eaa 100644
--- a/crypto/bn/bn_rand.c
+++ b/crypto/bn/bn_rand.c
@@ -122,6 +122,11 @@ 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;
@@ -168,7 +173,7 @@ static int bnrand(int pseudorand, BIGNUM *rnd, int bits, int top, int bottom)
         }
     }
 
-    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 d6b975ccf64385a96b5c880e4ddab4a5cf725dda..bd6bc8632394edb05908556338aa82dd7b1f977d 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