diff --git a/src/uint/ref_type/div.rs b/src/uint/ref_type/div.rs
index c2d63450..3cc467e3 100644
--- a/src/uint/ref_type/div.rs
+++ b/src/uint/ref_type/div.rs
@@ -620,7 +620,7 @@ impl UintRef {
 
         // Check that the dividend evenly divides by 2^tz, and shift it to match the divisor
         let div2s_exact = self.ensure_trailing_zeros(tz).and(excess_z.not());
-        self.shr_assign(tz);
+        self.unbounded_shr_assign(tz);
 
         let y = Odd::new_ref_unchecked(rhs);
         let y_inv = y.invert_mod_limb();
@@ -743,8 +743,12 @@ impl UintRef {
     const fn ensure_trailing_zeros(&self, zs: u32) -> Choice {
         let z_words = (zs >> Limb::LOG2_BITS) as usize;
         let z_bits = zs & (Limb::BITS - 1);
-        self.leading(z_words)
-            .is_zero()
-            .and(self.limbs[z_words].restrict_bits(z_bits).is_zero())
+        if z_words >= self.nlimbs() {
+            self.is_zero()
+        } else {
+            self.leading(z_words)
+                .is_zero()
+                .and(self.limbs[z_words].restrict_bits(z_bits).is_zero())
+        }
     }
 }
diff --git a/tests/uint.rs b/tests/uint.rs
index f82285ae..aee42e53 100644
--- a/tests/uint.rs
+++ b/tests/uint.rs
@@ -8,7 +8,7 @@ mod common;
 use common::to_biguint;
 use core::mem;
 use crypto_bigint::{
-    Encoding, Limb, NonZero, Odd, U256, U512, U4096, U8192, Uint, Word,
+    Encoding, Limb, NonZero, Odd, U128, U256, U512, U4096, U8192, Uint, Word,
     modular::{FixedMontyForm, FixedMontyParams},
 };
 use num_bigint::BigUint;
@@ -617,3 +617,12 @@ proptest! {
         prop_assert_eq!(expected, actual);
     }
 }
+
+#[test]
+fn div_exact_wide_power_of_two_divisor_is_inexact() {
+    let lhs = U128::ONE;
+    let rhs = NonZero::new(U256::ONE << U128::BITS).unwrap();
+
+    assert!(bool::from(lhs.div_exact(&rhs).is_none()));
+    assert!(bool::from(lhs.div_exact_vartime(&rhs).is_none()));
+}