diff --git a/src/hazmat/miller_rabin.rs b/src/hazmat/miller_rabin.rs
index 50d7ae6..4f70812 100644
--- a/src/hazmat/miller_rabin.rs
+++ b/src/hazmat/miller_rabin.rs
@@ -122,7 +122,7 @@ mod tests {
     use alloc::format;
     use core::num::NonZeroU32;
 
-    use crypto_bigint::{Integer, Odd, RandomMod, Uint, U1024, U128, U1536, U64};
+    use crypto_bigint::{Integer, Odd, RandomMod, Uint, U1024, U128, U1536, U256, U64};
     use rand_chacha::ChaCha8Rng;
     use rand_core::{CryptoRngCore, OsRng, SeedableRng};
 
@@ -280,6 +280,15 @@ mod tests {
         test_large_primes(primes::PRIMES_1024);
     }
 
+    // Test to guard against regressions such as https://github.com/RustCrypto/crypto-bigint/pull/685
+    #[test]
+    fn zero_padded_input_works() {
+        // A prime that happens to have 128 starting zeroes.
+        let hex = "00000000000000000000000000000000E0BD7D7A037746B47ABDDC706525370F";
+        let num = U256::from_be_hex(hex);
+        test_large_primes(&[num]);
+    }
+
     #[cfg(feature = "tests-exhaustive")]
     #[test]
     fn exhaustive() {
diff --git a/src/presets.rs b/src/presets.rs
index 30a1e75..2e2a2b5 100644
--- a/src/presets.rs
+++ b/src/presets.rs
@@ -189,10 +189,9 @@ fn _is_prime_with_rng<T: Integer + RandomMod>(rng: &mut impl CryptoRngCore, num:
 
 #[cfg(test)]
 mod tests {
-    use crypto_bigint::{BoxedUint, CheckedAdd, Uint, Word, U128, U256, U64};
+    use crypto_bigint::{BoxedUint, CheckedAdd, Uint, Word, U128, U64};
     use num_prime::nt_funcs::is_prime64;
-    use rand_chacha::ChaCha8Rng;
-    use rand_core::{OsRng, SeedableRng};
+    use rand_core::OsRng;
 
     use super::{
         generate_prime, generate_prime_with_rng, generate_safe_prime, generate_safe_prime_with_rng,
@@ -381,12 +380,6 @@ mod tests {
             }
         }
     }
-
-    #[test]
-    fn generate_prime_into_int_double_size_precision() {
-        let mut rng = ChaCha8Rng::from_seed(*b"01234567890123456789012345678901");
-        let _p = generate_safe_prime_with_rng::<U256>(&mut rng, 128, 256);
-    }
 }
 
 #[cfg(test)]