diff --git a/lib/srfi/27/rand.c b/lib/srfi/27/rand.c
index 13d4cc4d..678ecbfc 100644
--- a/lib/srfi/27/rand.c
+++ b/lib/srfi/27/rand.c
@@ -49,8 +49,9 @@ static sexp sexp_rs_random_integer (sexp ctx, sexp self, sexp_sint_t n, sexp rs,
   sexp res;
   sexp_int32_t m;
 #if SEXP_USE_BIGNUMS
-  sexp_uint32_t mod;
-  sexp_int32_t hi, len, i, *data;
+  sexp_uint_t mod;
+  sexp_uint32_t *data;
+  sexp_int32_t hi, len, i;
 #endif
   if (! sexp_random_source_p(rs))
     res = sexp_type_exception(ctx, self, rs_type_id, rs);
@@ -62,21 +63,35 @@ static sexp sexp_rs_random_integer (sexp ctx, sexp self, sexp_sint_t n, sexp rs,
     hi = sexp_bignum_hi(bound);
     len = hi * (sizeof(sexp_uint_t) / sizeof(sexp_int32_t));
     res = sexp_make_bignum(ctx, hi + 1);
-    data = (sexp_int32_t*) sexp_bignum_data(res);
-    for (i=0; i<len-1; i++) {
+    data = (sexp_uint32_t*) sexp_bignum_data(res);
+    for (i=0; i<len; i++) {
       sexp_call_random(rs, m);
       data[i] = m;
     }
     /* Scan down, modding bigits > bound to < bound, and stop as */
     /* soon as we are sure the result is within bound. */
-    for (i = hi-1; i >= 0; i--) {
+    for (i = hi-1; i >= 0; --i) {
       mod = sexp_bignum_data(bound)[i];
-      if (mod && sexp_bignum_data(res)[i] > mod) {
-        sexp_bignum_data(res)[i] %= mod;
+      if (mod) {
+        if (i > 0 && mod < SEXP_UINT_T_MAX) {
+          /* allow non-final bigits to be == */
+          ++mod;
+        }
+        if (sexp_bignum_data(res)[i] >= mod)
+          sexp_bignum_data(res)[i] %= mod;
+      } else {
+        sexp_bignum_data(res)[i] = 0;
       }
-      if (sexp_bignum_data(res)[i] != mod) {
+      if (sexp_bignum_data(res)[i] < sexp_bignum_data(bound)[i]) {
         break;
       }
+      if (i == 0) {
+        /* handle the case where all bigits are == */
+        if (sexp_bignum_data(res)[i] > 0)
+          --sexp_bignum_data(res)[i];
+        else
+          res = sexp_sub(ctx, res, SEXP_ONE);
+      }
     }
 #endif
   } else {