diff --git a/src/copy_bidirectional.rs b/src/copy_bidirectional.rs
index cdf12ee..71fee38 100644
--- a/src/copy_bidirectional.rs
+++ b/src/copy_bidirectional.rs
@@ -17,6 +17,7 @@ use std::task::{Context, Poll};
 #[derive(Debug)]
 struct CopyBuffer {
     read_done: bool,
+    need_flush: bool,
     start_index: usize,
     cache_length: usize,
     size: usize,
@@ -31,6 +32,7 @@ impl CopyBuffer {
         }
         Self {
             read_done: false,
+            need_flush: false,
             start_index: 0,
             cache_length: 0,
             size,
@@ -50,6 +52,7 @@ impl CopyBuffer {
     {
         loop {
             let mut read_pending = false;
+            let mut write_pending = false;
 
             // If our buffer has some space, let's read up!
             if !self.read_done && self.cache_length < self.size {
@@ -74,6 +77,8 @@ impl CopyBuffer {
                         }
                     }
                     Poll::Pending => {
+                        // Try flushing when the reader has no progress to avoid deadlock
+                        // when the reader depends on buffered writer.
                         read_pending = true;
                     }
                 }
@@ -107,25 +112,30 @@ impl CopyBuffer {
                             } else {
                                 self.start_index = (self.start_index + written) % self.size;
                             }
+                            self.need_flush = true;
                         }
                     }
                     Poll::Pending => {
-                        // Previously we set a write_pending flag, and kept going until
-                        // both read and write were pending, but this might starve other
-                        // tasks.
-                        return Poll::Pending;
+                        write_pending = true;
+                        break;
                     }
                 }
             }
 
+            if self.need_flush {
+                ready!(writer.as_mut().poll_flush(cx))?;
+                self.need_flush = false;
+            }
+
             // If we've written all the data and we've seen EOF, flush out the
             // data and finish the transfer.
             if self.read_done && self.cache_length == 0 {
-                ready!(writer.as_mut().poll_flush(cx))?;
                 return Poll::Ready(Ok(()));
             }
 
-            if read_pending {
+            // Previously we kept going until both read and write were pending, but
+            // this might starve other tasks.
+            if read_pending || write_pending {
                 // If we got here,
                 // 1) we hit read_pending on the current iteration.
                 // 2) all data has been written successfully