diff --git a/tokio-postgres/src/client.rs b/tokio-postgres/src/client.rs
index 8fe8090a3..8c3c04fc8 100644
--- a/tokio-postgres/src/client.rs
+++ b/tokio-postgres/src/client.rs
@@ -113,7 +113,7 @@ pub struct InnerClient {
 
 impl InnerClient {
     pub fn send(&self, messages: RequestMessages) -> Result<Responses, Error> {
-        let (sender, receiver) = mpsc::channel(1);
+        let (sender, receiver) = mpsc::channel(1024);
         let request = Request { messages, sender };
         self.sender
             .unbounded_send(request)
diff --git a/tokio-postgres/src/copy_in.rs b/tokio-postgres/src/copy_in.rs
index 8cdb817ac..4e786e564 100644
--- a/tokio-postgres/src/copy_in.rs
+++ b/tokio-postgres/src/copy_in.rs
@@ -192,7 +192,7 @@ async fn start<T>(client: &InnerClient, buf: Bytes, simple: bool) -> Result<Copy
 where
     T: Buf + 'static + Send,
 {
-    let (mut sender, receiver) = mpsc::channel(1);
+    let (mut sender, receiver) = mpsc::channel(1024);
     let receiver = CopyInReceiver::new(receiver);
     let mut responses = client.send(RequestMessages::CopyIn(receiver))?;