diff --git a/neqo-transport/src/connection/mod.rs b/neqo-transport/src/connection/mod.rs
index 8522507a69..f4e2847609 100644
--- a/neqo-transport/src/connection/mod.rs
+++ b/neqo-transport/src/connection/mod.rs
@@ -46,7 +46,7 @@ use crate::{
     quic_datagrams::{DatagramTracking, QuicDatagrams},
     recovery::{LossRecovery, RecoveryToken, SendProfile},
     recv_stream::RecvStreamStats,
-    rtt::GRANULARITY,
+    rtt::{RttEstimate, GRANULARITY},
     send_stream::SendStream,
     stats::{Stats, StatsCell},
     stream_id::StreamType,
@@ -610,11 +610,10 @@ impl Connection {
     /// a value of this approximate order.  Don't use this for loss recovery,
     /// only use it where a more precise value is not important.
     fn pto(&self) -> Duration {
-        self.paths
-            .primary()
-            .borrow()
-            .rtt()
-            .pto(PacketNumberSpace::ApplicationData)
+        self.paths.primary_fallible().map_or_else(
+            || RttEstimate::default().pto(PacketNumberSpace::ApplicationData),
+            |p| p.borrow().rtt().pto(PacketNumberSpace::ApplicationData),
+        )
     }
 
     fn create_resumption_token(&mut self, now: Instant) {
@@ -962,9 +961,11 @@ impl Connection {
         let res = self.crypto.states.check_key_update(now);
         self.absorb_error(now, res);
 
-        let lost = self.loss_recovery.timeout(&self.paths.primary(), now);
-        self.handle_lost_packets(&lost);
-        qlog::packets_lost(&mut self.qlog, &lost);
+        if let Some(path) = self.paths.primary_fallible() {
+            let lost = self.loss_recovery.timeout(&path, now);
+            self.handle_lost_packets(&lost);
+            qlog::packets_lost(&mut self.qlog, &lost);
+        }
 
         if self.release_resumption_token_timer.is_some() {
             self.create_resumption_token(now);
@@ -2861,8 +2862,11 @@ impl Connection {
     {
         qdebug!([self], "Rx ACK space={}, ranges={:?}", space, ack_ranges);
 
+        let Some(path) = self.paths.primary_fallible() else {
+            return;
+        };
         let (acked_packets, lost_packets) = self.loss_recovery.on_ack_received(
-            &self.paths.primary(),
+            &path,
             space,
             largest_acknowledged,
             ack_ranges,
diff --git a/neqo-transport/tests/server.rs b/neqo-transport/tests/server.rs
index 7388e0fee7..745ee79520 100644
--- a/neqo-transport/tests/server.rs
+++ b/neqo-transport/tests/server.rs
@@ -477,6 +477,65 @@ fn bad_client_initial() {
     assert_eq!(res, Output::None);
 }
 
+#[test]
+fn bad_client_initial_connection_close() {
+    let mut client = default_client();
+    let mut server = default_server();
+
+    let dgram = client.process(None, now()).dgram().expect("a datagram");
+    let (header, d_cid, s_cid, payload) = decode_initial_header(&dgram, Role::Client);
+    let (aead, hp) = initial_aead_and_hp(d_cid, Role::Client);
+    let (_, pn) = remove_header_protection(&hp, header, payload);
+
+    let mut payload_enc = Encoder::with_capacity(1200);
+    payload_enc.encode(&[0x1c, 0x01, 0x00, 0x00]); // Add a CONNECTION_CLOSE frame.
+
+    // Make a new header with a 1 byte packet number length.
+    let mut header_enc = Encoder::new();
+    header_enc
+        .encode_byte(0xc0) // Initial with 1 byte packet number.
+        .encode_uint(4, Version::default().wire_version())
+        .encode_vec(1, d_cid)
+        .encode_vec(1, s_cid)
+        .encode_vvec(&[])
+        .encode_varint(u64::try_from(payload_enc.len() + aead.expansion() + 1).unwrap())
+        .encode_byte(u8::try_from(pn).unwrap());
+
+    let mut ciphertext = header_enc.as_ref().to_vec();
+    ciphertext.resize(header_enc.len() + payload_enc.len() + aead.expansion(), 0);
+    let v = aead
+        .encrypt(
+            pn,
+            header_enc.as_ref(),
+            payload_enc.as_ref(),
+            &mut ciphertext[header_enc.len()..],
+        )
+        .unwrap();
+    assert_eq!(header_enc.len() + v.len(), ciphertext.len());
+    // Pad with zero to get up to 1200.
+    ciphertext.resize(1200, 0);
+
+    apply_header_protection(
+        &hp,
+        &mut ciphertext,
+        (header_enc.len() - 1)..header_enc.len(),
+    );
+    let bad_dgram = Datagram::new(
+        dgram.source(),
+        dgram.destination(),
+        dgram.tos(),
+        dgram.ttl(),
+        ciphertext,
+    );
+
+    // The server should ignore this and go to Draining.
+    let mut now = now();
+    let response = server.process(Some(&bad_dgram), now);
+    now += response.callback();
+    let response = server.process(None, now);
+    assert_eq!(response, Output::None);
+}
+
 #[test]
 fn version_negotiation_ignored() {
     let mut server = default_server();