diff --git a/coordinator/src/p2p.rs b/coordinator/src/p2p.rs
index 627af966..cce96d86 100644
--- a/coordinator/src/p2p.rs
+++ b/coordinator/src/p2p.rs
@@ -558,6 +558,17 @@ impl TributaryP2p for LibP2p {
   }
 }
 
+fn heartbeat_time_unit<D: Db, P: P2p>() -> u64 {
+  // Also include the timestamp so LibP2p doesn't flag this as an old message re-circulating
+  let timestamp = SystemTime::now()
+    .duration_since(SystemTime::UNIX_EPOCH)
+    .expect("system clock is wrong")
+    .as_secs();
+  // Divide by the block time so if multiple parties send a Heartbeat, they're more likely to
+  // overlap
+  timestamp / u64::from(Tributary::<D, Transaction, P>::block_time())
+}
+
 pub async fn heartbeat_tributaries_task<D: Db, P: P2p>(
   p2p: P,
   mut tributary_event: broadcast::Receiver<TributaryEvent<D, P>>,
@@ -592,14 +603,7 @@ pub async fn heartbeat_tributaries_task<D: Db, P: P2p>(
       if SystemTime::now() > (block_time + Duration::from_secs(60)) {
         log::warn!("last known tributary block was over a minute ago");
         let mut msg = tip.to_vec();
-        // Also include the timestamp so LibP2p doesn't flag this as an old message re-circulating
-        let timestamp = SystemTime::now()
-          .duration_since(SystemTime::UNIX_EPOCH)
-          .expect("system clock is wrong")
-          .as_secs();
-        // Divide by the block time so if multiple parties send a Heartbeat, they're more likely to
-        // overlap
-        let time_unit = timestamp / u64::from(Tributary::<D, Transaction, P>::block_time());
+        let time_unit = heartbeat_time_unit::<D, P>();
         msg.extend(time_unit.to_le_bytes());
         P2p::broadcast(&p2p, P2pMessageKind::Heartbeat(tributary.genesis()), msg).await;
       }
@@ -666,6 +670,13 @@ pub async fn handle_p2p_task<D: Db, P: P2p>(
                         log::error!("validator sent invalid heartbeat");
                         continue;
                       }
+                      // Only respond to recent heartbeats
+                      let msg_time_unit = u64::from_le_bytes(msg.msg[32 .. 40].try_into().expect(
+                        "length-checked heartbeat message didn't have 8 bytes for the u64",
+                      ));
+                      if heartbeat_time_unit::<D, P>().saturating_sub(msg_time_unit) > 1 {
+                        continue;
+                      }
 
                       let p2p = p2p.clone();
                       let spec = tributary.spec.clone();
@@ -715,7 +726,7 @@ pub async fn handle_p2p_task<D: Db, P: P2p>(
                           to_send.push(next);
                           latest = next;
                         }
-                        if to_send.len() > 1 {
+                        if to_send.len() > 3 {
                           for next in to_send {
                             let mut res = reader.block(&next).unwrap().serialize();
                             res.extend(reader.commit(&next).unwrap());