diff --git a/tokio-postgres/src/copy_both.rs b/tokio-postgres/src/copy_both.rs
index d3b46eab7..e8c2103b0 100644
--- a/tokio-postgres/src/copy_both.rs
+++ b/tokio-postgres/src/copy_both.rs
@@ -16,6 +16,9 @@ use std::task::{Context, Poll};
 /// The state machine of CopyBothReceiver
 ///
 /// ```ignore
+///       Setup
+///         |
+///         v
 ///      CopyBoth
 ///       /   \
 ///      v     v
@@ -189,17 +192,27 @@ impl Stream for CopyBothReceiver {
             Poll::Pending => match self.state {
                 Setup | CopyBoth | CopyIn => match ready!(self.sink_receiver.poll_next_unpin(cx)) {
                     Some(msg) => Poll::Ready(Some(msg)),
-                    None => {
-                        self.state = match self.state {
-                            CopyBoth => CopyOut,
-                            CopyIn => CopyNone,
-                            _ => unreachable!(),
-                        };
-
-                        let mut buf = BytesMut::new();
-                        frontend::copy_done(&mut buf);
-                        Poll::Ready(Some(FrontendMessage::Raw(buf.freeze())))
-                    }
+                    None => match self.state {
+                        // The user has cancelled their interest to this CopyBoth query but we're
+                        // still in the Setup phase. From this point the receiver will either enter
+                        // CopyBoth mode or will receive an Error response from PostgreSQL. When
+                        // either of those happens the state machine will terminate the connection
+                        // appropriately.
+                        Setup => Poll::Pending,
+                        CopyBoth => {
+                            self.state = CopyOut;
+                            let mut buf = BytesMut::new();
+                            frontend::copy_done(&mut buf);
+                            Poll::Ready(Some(FrontendMessage::Raw(buf.freeze())))
+                        }
+                        CopyIn => {
+                            self.state = CopyNone;
+                            let mut buf = BytesMut::new();
+                            frontend::copy_done(&mut buf);
+                            Poll::Ready(Some(FrontendMessage::Raw(buf.freeze())))
+                        }
+                        _ => unreachable!(),
+                    },
                 },
                 _ => Poll::Pending,
             },