diff --git a/src/fns/unconstrained_helpers.nr b/src/fns/unconstrained_helpers.nr
index 0afcfb40..28eee2f3 100644
--- a/src/fns/unconstrained_helpers.nr
+++ b/src/fns/unconstrained_helpers.nr
@@ -39,12 +39,11 @@ pub(crate) unconstrained fn __validate_gt_remainder<let N: u32>(
     let mut b_u60: U60Repr<N, 2> = U60Repr::from(rhs);
 
     let underflow = b_u60.gte(a_u60);
-    b_u60 += U60Repr::one();
     assert(underflow == false, "BigNum::validate_gt check fails");
     let mut result_u60: U60Repr<N, 2> = U60Repr { limbs: [0; 2 * N] };
 
     let mut carry_in: u64 = 0;
-    let mut borrow_in: u64 = 0;
+    let mut borrow_in: u64 = 1;
     let mut borrow_flags: [bool; N] = [false; N];
     let mut carry_flags: [bool; N] = [false; N];
     for i in 0..2 * N {
diff --git a/src/fns/unconstrained_ops.nr b/src/fns/unconstrained_ops.nr
index 68e12df0..86711fe7 100644
--- a/src/fns/unconstrained_ops.nr
+++ b/src/fns/unconstrained_ops.nr
@@ -171,34 +171,40 @@ pub(crate) unconstrained fn __udiv_mod<let N: u32>(
     let mut divisor_u60: U60Repr<N, 2> = U60Repr::from(divisor);
     let b = divisor_u60;
 
-    let mut bit_difference = remainder_u60.get_msb() - divisor_u60.get_msb();
+    let numerator_msb = remainder_u60.get_msb();
+    let divisor_msb = divisor_u60.get_msb();
+    if divisor_msb > numerator_msb {
+        ([0; N], numerator)
+    } else {
+        let mut bit_difference = numerator_msb - divisor_msb;
 
-    let mut accumulator_u60: U60Repr<N, 2> = U60Repr::one();
-    divisor_u60 = divisor_u60.shl(bit_difference);
-    accumulator_u60 = accumulator_u60.shl(bit_difference);
+        let mut accumulator_u60: U60Repr<N, 2> = U60Repr::one();
+        divisor_u60 = divisor_u60.shl(bit_difference);
+        accumulator_u60 = accumulator_u60.shl(bit_difference);
 
-    if (divisor_u60.gte(remainder_u60 + U60Repr::one())) {
-        divisor_u60.shr1();
-        accumulator_u60.shr1();
-    }
-    for _ in 0..(N * 120) {
-        if (remainder_u60.gte(b) == false) {
-            break;
+        if (divisor_u60.gte(remainder_u60 + U60Repr::one())) {
+            divisor_u60.shr1();
+            accumulator_u60.shr1();
         }
+        for _ in 0..(N * 120) {
+            if (remainder_u60.gte(b) == false) {
+                break;
+            }
 
-        // we've shunted 'divisor' up to have the same bit length as our remainder.
-        // If remainder >= divisor, then a is at least '1 << bit_difference' multiples of b
-        if (remainder_u60.gte(divisor_u60)) {
-            remainder_u60 -= divisor_u60;
-            // we can use OR here instead of +, as
-            // accumulator is always a nice power of two
-            quotient_u60 = quotient_u60 + accumulator_u60;
+            // we've shunted 'divisor' up to have the same bit length as our remainder.
+            // If remainder >= divisor, then a is at least '1 << bit_difference' multiples of b
+            if (remainder_u60.gte(divisor_u60)) {
+                remainder_u60 -= divisor_u60;
+                // we can use OR here instead of +, as
+                // accumulator is always a nice power of two
+                quotient_u60 = quotient_u60 + accumulator_u60;
+            }
+            divisor_u60.shr1(); // >>= 1;
+            accumulator_u60.shr1(); //  >>= 1;
         }
-        divisor_u60.shr1(); // >>= 1;
-        accumulator_u60.shr1(); //  >>= 1;
-    }
 
-    (U60Repr::into(quotient_u60), U60Repr::into(remainder_u60))
+        (U60Repr::into(quotient_u60), U60Repr::into(remainder_u60))
+    }
 }
 
 pub(crate) unconstrained fn __invmod<let N: u32, let MOD_BITS: u32>(
diff --git a/src/tests/bignum_test.nr b/src/tests/bignum_test.nr
index ffc8f524..c16c136d 100644
--- a/src/tests/bignum_test.nr
+++ b/src/tests/bignum_test.nr
@@ -632,6 +632,21 @@ fn test_udiv_mod_U256() {
     assert(product == a);
 }
 
+#[test]
+fn test_1_udiv_mod_2() {
+    let _0: U256 = BigNum::new();
+    let _1: U256 = BigNum::one();
+    assert(_1.udiv_mod(_1 + _1) == (_0, _1));
+}
+
+#[test]
+fn test_20_udiv_mod_11() {
+    let _1: U256 = BigNum::one();
+    let _2_POW_120: U256 = BigNum::from_slice([0, 1, 0]);
+    let _2_POW_121: U256 = BigNum::from_slice([0, 2, 0]);
+    assert(_2_POW_121.udiv_mod(_2_POW_120 + _1) == (_1, _2_POW_120 - _1));
+}
+
 // // N.B. witness generation times make these tests take ~15 minutes each! Uncomment at your peril
 // #[test]
 // fn test_div_2048() {