diff --git a/proxy/src/proxy/copy_bidirectional.rs b/proxy/src/proxy/copy_bidirectional.rs
index 3336a9556a..861f1766e8 100644
--- a/proxy/src/proxy/copy_bidirectional.rs
+++ b/proxy/src/proxy/copy_bidirectional.rs
@@ -201,25 +201,26 @@ impl CopyBuffer {
         W: AsyncWrite + ?Sized,
     {
         loop {
-            // If our buffer is empty, then we need to read some data to
-            // continue.
-            if self.pos == self.cap && !self.read_done {
-                self.pos = 0;
-                self.cap = 0;
-
+            // If there is some space left in our buffer, then we try to read some
+            // data to continue, thus maximizing the chances of a large write.
+            if self.cap < self.buf.len() && !self.read_done {
                 match self.poll_fill_buf(cx, reader.as_mut()) {
                     Poll::Ready(Ok(())) => (),
                     Poll::Ready(Err(err)) => return Poll::Ready(Err(ErrorDirection::Read(err))),
                     Poll::Pending => {
-                        // Try flushing when the reader has no progress to avoid deadlock
-                        // when the reader depends on buffered writer.
-                        if self.need_flush {
-                            ready!(writer.as_mut().poll_flush(cx))
-                                .map_err(ErrorDirection::Write)?;
-                            self.need_flush = false;
-                        }
+                        // Ignore pending reads when our buffer is not empty, because
+                        // we can try to write data immediately.
+                        if self.pos == self.cap {
+                            // Try flushing when the reader has no progress to avoid deadlock
+                            // when the reader depends on buffered writer.
+                            if self.need_flush {
+                                ready!(writer.as_mut().poll_flush(cx))
+                                    .map_err(ErrorDirection::Write)?;
+                                self.need_flush = false;
+                            }
 
-                        return Poll::Pending;
+                            return Poll::Pending;
+                        }
                     }
                 }
             }
@@ -246,9 +247,13 @@ impl CopyBuffer {
                 "writer returned length larger than input slice"
             );
 
+            // All data has been written, the buffer can be considered empty again
+            self.pos = 0;
+            self.cap = 0;
+
             // If we've written all the data and we've seen EOF, flush out the
             // data and finish the transfer.
-            if self.pos == self.cap && self.read_done {
+            if self.read_done {
                 ready!(writer.as_mut().poll_flush(cx)).map_err(ErrorDirection::Write)?;
                 return Poll::Ready(Ok(self.amt));
             }