diff --git a/tokio/src/io/util/copy.rs b/tokio/src/io/util/copy.rs
index 47f8d4ebe..4fcec9075 100644
--- a/tokio/src/io/util/copy.rs
+++ b/tokio/src/io/util/copy.rs
@@ -96,12 +96,9 @@ impl CopyBuffer {
         // Keep track of task budget
         let coop = ready!(crate::runtime::coop::poll_proceed(cx));
         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(())) => {
                         #[cfg(any(
@@ -131,25 +128,29 @@ impl CopyBuffer {
                         return Poll::Ready(Err(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))?;
-                            #[cfg(any(
-                                feature = "fs",
-                                feature = "io-std",
-                                feature = "net",
-                                feature = "process",
-                                feature = "rt",
-                                feature = "signal",
-                                feature = "sync",
-                                feature = "time",
-                            ))]
-                            coop.made_progress();
-                            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))?;
+                                #[cfg(any(
+                                    feature = "fs",
+                                    feature = "io-std",
+                                    feature = "net",
+                                    feature = "process",
+                                    feature = "rt",
+                                    feature = "signal",
+                                    feature = "sync",
+                                    feature = "time",
+                                ))]
+                                coop.made_progress();
+                                self.need_flush = false;
+                            }
 
-                        return Poll::Pending;
+                            return Poll::Pending;
+                        }
                     }
                 }
             }
@@ -188,9 +189,13 @@ 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))?;
                 #[cfg(any(
                     feature = "fs",