diff --git a/src/kx.rs b/src/kx.rs
index 3f8a4dd..999dab3 100644
--- a/src/kx.rs
+++ b/src/kx.rs
@@ -33,11 +33,15 @@ impl crypto::ActiveKeyExchange for X25519KeyExchange {
         let peer_array: [u8; 32] = peer
             .try_into()
             .map_err(|_| rustls::Error::from(rustls::PeerMisbehaved::InvalidKeyShare))?;
-        Ok(self
-            .priv_key
-            .diffie_hellman(&peer_array.into())
-            .as_ref()
-            .into())
+        let shared = self.priv_key.diffie_hellman(&peer_array.into());
+        // RFC 8446 §4.2.8.2: a peer key of low order makes this result the
+        // identity — a secret the peer knows. `x25519-dalek` only *reports* that
+        // through `was_contributory`, and `complete` is documented as the place an
+        // invalid share has to be rejected.
+        if !shared.was_contributory() {
+            return Err(rustls::Error::from(rustls::PeerMisbehaved::InvalidKeyShare));
+        }
+        Ok(shared.as_ref().into())
     }
 
     fn pub_key(&self) -> &[u8] {
diff --git a/tests/x25519_low_order.rs b/tests/x25519_low_order.rs
new file mode 100644
index 0000000..427c2da
--- /dev/null
+++ b/tests/x25519_low_order.rs
@@ -0,0 +1,110 @@
+//! RFC 8446 §4.2.8.2 for the provider's X25519 group: a peer key of low order
+//! makes the Diffie-Hellman result the identity — a shared secret the peer knows —
+//! and `x25519-dalek` only *reports* that through `was_contributory()`, so the
+//! group is the only place the rejection can be made. The trait asks for exactly
+//! that ("must return an error if `peer_pub_key` is invalid: ... such as, but not
+//! limited to, being in a small order subgroup"), and the `ring` and `aws-lc-rs`
+//! providers do it.
+
+use rustls::crypto::SupportedKxGroup;
+use rustls::{Error, NamedGroup, PeerMisbehaved};
+use rustls_rustcrypto::provider;
+
+/// The seven encodings of a low-order point, from libsodium's `has_small_order`
+/// table: the points of order 1, 2, 4 and 8, and the three non-canonical encodings
+/// at or above the field prime that reduce to them. Each of them is a valid
+/// Curve25519 public key whose shared secret is the identity, so a check that only
+/// rejected the all-zero key would still accept a key of order 2.
+const LOW_ORDER_PEER_KEYS: [[u8; 32]; 7] = [
+    // 0 (order 4)
+    [0; 32],
+    // 1 (order 1)
+    [
+        1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+        0, 0,
+    ],
+    // order 8
+    [
+        0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4,
+        0x6a, 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd, 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49,
+        0xb8, 0x00,
+    ],
+    // order 8
+    [
+        0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24, 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef,
+        0x5b, 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86, 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f,
+        0x11, 0x57,
+    ],
+    // p - 1 (order 2)
+    [
+        0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0x7f,
+    ],
+    // p (order 4), non-canonical
+    [
+        0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0x7f,
+    ],
+    // p + 1 (order 1), non-canonical
+    [
+        0xee, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0x7f,
+    ],
+];
+
+fn x25519() -> &'static dyn SupportedKxGroup {
+    provider()
+        .kx_groups
+        .into_iter()
+        .find(|group| group.name() == NamedGroup::X25519)
+        .expect("the provider offers X25519")
+}
+
+/// Every low-order peer key aborts, with the key-share error `complete` documents.
+#[test]
+fn x25519_rejects_a_low_order_peer_key() {
+    for peer_key in LOW_ORDER_PEER_KEYS {
+        let active = x25519().start().expect("a key exchange starts");
+        match active.complete(&peer_key) {
+            Ok(secret) => panic!(
+                "a low-order peer key was accepted: {peer_key:02x?} -> {} bytes",
+                secret.secret_bytes().len()
+            ),
+            Err(err) => assert!(
+                matches!(err, Error::PeerMisbehaved(PeerMisbehaved::InvalidKeyShare)),
+                "unexpected error for {peer_key:02x?}: {err:?}"
+            ),
+        }
+    }
+}
+
+/// A peer key that is not 32 bytes is the same key-share error, not a panic.
+#[test]
+fn x25519_rejects_a_peer_key_of_the_wrong_length() {
+    let active = x25519().start().expect("a key exchange starts");
+    assert!(matches!(
+        active.complete(&[0u8; 31]),
+        Err(Error::PeerMisbehaved(PeerMisbehaved::InvalidKeyShare))
+    ));
+}
+
+/// The control for the two tests above: a real peer key completes, with a 32-byte
+/// secret that is not the identity. Without it, a group that rejected every key
+/// would pass them too.
+#[test]
+fn x25519_completes_for_a_real_peer_key() {
+    let active = x25519().start().expect("a key exchange starts");
+    let peer = x25519().start().expect("a key exchange starts");
+    let peer_key = peer.pub_key().to_vec();
+    let secret = active
+        .complete(&peer_key)
+        .expect("a real peer key completes");
+    assert_eq!(secret.secret_bytes().len(), 32);
+    assert!(
+        secret.secret_bytes().iter().any(|byte| *byte != 0),
+        "the identity is not a completed key exchange"
+    );
+}