diff --git a/zebra-network/src/peer/connector.rs b/zebra-network/src/peer/connector.rs
index 1bf58be5f..7c1633c90 100644
--- a/zebra-network/src/peer/connector.rs
+++ b/zebra-network/src/peer/connector.rs
@@ -11,7 +11,7 @@ use tower::{discover::Change, Service, ServiceExt};
 
 use crate::{BoxedStdError, Request, Response};
 
-use super::{Client, Handshake, HandshakeError};
+use super::{Client, Handshake};
 
 /// A wrapper around [`peer::Handshake`] that opens a TCP connection before
 /// forwarding to the inner handshake service. Writing this as its own
@@ -40,7 +40,7 @@ where
     S::Future: Send,
 {
     type Response = Change<SocketAddr, Client>;
-    type Error = HandshakeError;
+    type Error = BoxedStdError;
     type Future =
         Pin<Box<dyn Future<Output = Result<Self::Response, Self::Error>> + Send + 'static>>;
 
diff --git a/zebra-network/src/peer/handshake.rs b/zebra-network/src/peer/handshake.rs
index c917aa3b3..4894977d8 100644
--- a/zebra-network/src/peer/handshake.rs
+++ b/zebra-network/src/peer/handshake.rs
@@ -80,7 +80,7 @@ where
     S::Future: Send,
 {
     type Response = Client;
-    type Error = HandshakeError;
+    type Error = BoxedStdError;
     type Future =
         Pin<Box<dyn Future<Output = Result<Self::Response, Self::Error>> + Send + 'static>>;
 
@@ -257,6 +257,16 @@ where
 
             Ok(client)
         };
-        fut.instrument(connector_span).boxed()
+
+        // Spawn a new task to drive this handshake.
+        tokio::spawn(fut.instrument(connector_span))
+            // This is required to get error types to line up.
+            // Probably there's a nicer way to express this using combinators.
+            .map(|x| match x {
+                Ok(Ok(client)) => Ok(client),
+                Ok(Err(handshake_err)) => Err(handshake_err.into()),
+                Err(join_err) => Err(join_err.into()),
+            })
+            .boxed()
     }
 }