diff --git a/tokio-postgres/src/copy_both.rs b/tokio-postgres/src/copy_both.rs
index d3b46eab..e8c2103b 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,
             },
diff --git a/tokio-postgres/tests/test/copy_both.rs b/tokio-postgres/tests/test/copy_both.rs
index 2723928a..445d93c0 100644
--- a/tokio-postgres/tests/test/copy_both.rs
+++ b/tokio-postgres/tests/test/copy_both.rs
@@ -1,6 +1,8 @@
 use futures_util::{future, StreamExt, TryStreamExt};
 use tokio_postgres::{error::SqlState, Client, SimpleQueryMessage, SimpleQueryRow};
 
+use crate::Cancellable;
+
 async fn q(client: &Client, query: &str) -> Vec<SimpleQueryRow> {
     let msgs = client.simple_query(query).await.unwrap();
 
@@ -123,3 +125,36 @@ async fn copy_both() {
     // Ensure we can continue issuing queries
     assert_eq!(q(&client, "SELECT 1").await[0].get(0), Some("1"));
 }
+
+#[tokio::test]
+async fn copy_both_future_cancellation() {
+    let client = crate::connect("user=postgres replication=database").await;
+
+    let slot_query =
+        "CREATE_REPLICATION_SLOT future_cancellation TEMPORARY LOGICAL \"test_decoding\"";
+    let lsn = q(&client, slot_query).await[0]
+        .get("consistent_point")
+        .unwrap()
+        .to_owned();
+
+    let query = format!("START_REPLICATION SLOT future_cancellation LOGICAL {}", lsn);
+    for i in 0.. {
+        let done = {
+            let duplex_stream = client.copy_both_simple::<bytes::Bytes>(&query);
+            let fut = Cancellable {
+                fut: duplex_stream,
+                polls_left: i,
+            };
+            fut.await
+                .map(|res| res.expect("copy_both failed"))
+                .is_some()
+        };
+
+        // Ensure we can continue issuing queries
+        assert_eq!(q(&client, "SELECT 1").await[0].get(0), Some("1"));
+
+        if done {
+            break;
+        }
+    }
+}