diff --git a/tests/crt_coefficient.rs b/tests/crt_coefficient.rs
new file mode 100644
index 00000000..aa49bab3
--- /dev/null
+++ b/tests/crt_coefficient.rs
@@ -0,0 +1,71 @@
+//! Test CRT coefficients for primes with different storage precisions.
+
+use rsa::{traits::PrivateKeyParts, BoxedUint, RsaPrivateKey};
+
+fn key_and_coefficient(reverse: bool) -> (RsaPrivateKey, BoxedUint) {
+    let (p, q, expected) = if reverse {
+        // (2^127 - 1) mod 3 = 1.
+        (3u128, u128::MAX >> 1, 1u128)
+    } else {
+        // 3 * ((2^128 - 1) / 3) = 2p + 1.
+        (u128::MAX >> 1, 3u128, u128::MAX / 3)
+    };
+    let key = RsaPrivateKey::from_p_q(
+        BoxedUint::from(p),
+        BoxedUint::from(q),
+        BoxedUint::from(65537u64),
+    )
+    .unwrap();
+
+    assert_ne!(
+        key.primes()[0].bits_precision(),
+        key.primes()[1].bits_precision()
+    );
+    (key, BoxedUint::from(expected))
+}
+
+fn check_coefficient(reverse: bool) {
+    let (mut key, expected) = key_and_coefficient(reverse);
+    assert_eq!(key.crt_coefficient().unwrap(), expected);
+    key.clear_precomputed();
+    assert_eq!(key.crt_coefficient().unwrap(), expected);
+}
+
+#[test]
+fn crt_coefficient_wider_p() {
+    check_coefficient(false);
+}
+
+#[test]
+fn crt_coefficient_wider_q() {
+    check_coefficient(true);
+}
+
+#[cfg(feature = "encoding")]
+fn check_encoded_coefficient(reverse: bool) {
+    use pkcs1::{EncodeRsaPrivateKey, RsaPrivateKeyRef};
+    use pkcs8::der::Decode;
+
+    let (mut key, expected) = key_and_coefficient(reverse);
+    for clear_precomputed in [false, true] {
+        if clear_precomputed {
+            key.clear_precomputed();
+        }
+        let der = key.to_pkcs1_der().unwrap();
+        let encoded = RsaPrivateKeyRef::from_der(der.as_bytes()).unwrap();
+        let coefficient = BoxedUint::from_be_slice(encoded.coefficient.as_bytes(), 128).unwrap();
+        assert_eq!(coefficient, expected);
+    }
+}
+
+#[test]
+#[cfg(feature = "encoding")]
+fn pkcs1_coefficient_wider_p() {
+    check_encoded_coefficient(false);
+}
+
+#[test]
+#[cfg(feature = "encoding")]
+fn pkcs1_coefficient_wider_q() {
+    check_encoded_coefficient(true);
+}