diff --git a/mpint.c b/mpint.c
index 8ac7a50e..6113d179 100644
--- a/mpint.c
+++ b/mpint.c
@@ -869,11 +869,12 @@ unsigned mp_cmp_hs(mp_int *a, mp_int *b)
 unsigned mp_hs_integer(mp_int *x, uintmax_t n)
 {
     BignumInt carry = 1;
-    for (size_t i = 0; i < x->nw; i++) {
+    size_t nwords = sizeof(n)/BIGNUM_INT_BYTES;
+    for (size_t i = 0, e = size_t_max(x->nw, nwords); i < e; i++) {
         BignumInt nword = n;
         n = shift_right_by_one_word(n);
         BignumInt dummy_out;
-        BignumADC(dummy_out, carry, x->w[i], ~nword, carry);
+        BignumADC(dummy_out, carry, mp_word(x, i), ~nword, carry);
         (void)dummy_out;
     }
     return carry;
@@ -895,10 +896,11 @@ unsigned mp_cmp_eq(mp_int *a, mp_int *b)
 unsigned mp_eq_integer(mp_int *x, uintmax_t n)
 {
     BignumInt diff = 0;
-    for (size_t i = 0; i < x->nw; i++) {
+    size_t nwords = sizeof(n)/BIGNUM_INT_BYTES;
+    for (size_t i = 0, e = size_t_max(x->nw, nwords); i < e; i++) {
         BignumInt nword = n;
         n = shift_right_by_one_word(n);
-        diff |= x->w[i] ^ nword;
+        diff |= mp_word(x, i) ^ nword;
     }
     return 1 ^ normalise_to_1(diff);   /* return 1 if diff _is_ zero */
 }
diff --git a/test/cryptsuite.py b/test/cryptsuite.py
index 995110b0..5564c11f 100755
--- a/test/cryptsuite.py
+++ b/test/cryptsuite.py
@@ -252,6 +252,19 @@ class mpint(MyTestBase):
                 mp_max_into(am_big, am, bm)
                 self.assertEqual(int(am_big), max(ai, bi))
 
+        # Test mp_{eq,hs}_integer in the case where the integer is as
+        # large as possible and the bignum contains very few words. In
+        # modes where BIGNUM_INT_BITS < 64, this used to go wrong.
+        mp10 = mp_new(4)
+        mp_add_integer_into(mp10, mp10, 10)
+        highbit = 1 << 63
+        self.assertEqual(mp_hs_integer(mp10, highbit | 9), 0)
+        self.assertEqual(mp_hs_integer(mp10, highbit | 10), 0)
+        self.assertEqual(mp_hs_integer(mp10, highbit | 11), 0)
+        self.assertEqual(mp_eq_integer(mp10, highbit | 9), 0)
+        self.assertEqual(mp_eq_integer(mp10, highbit | 10), 0)
+        self.assertEqual(mp_eq_integer(mp10, highbit | 11), 0)
+
     def testConditionals(self):
         testnumbers = [(mp_copy(n),n) for n in fibonacci_scattered()]
         for am, ai in testnumbers: