diff --git a/Cargo.toml b/Cargo.toml
index 23bb8f5..aff168f 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -14,8 +14,8 @@ An implementation of SSL streams for Tokio backed by OpenSSL
 [dependencies]
 openssl = "0.10.30"
 openssl-sys = "0.9.58"
-tokio = "0.2"
+tokio = "0.3"
 
 [dev-dependencies]
 futures = "0.3"
-tokio = { version = "0.2", features = ["full"] }
+tokio = { version = "0.3", features = ["full"] }
diff --git a/src/lib.rs b/src/lib.rs
index ba42fe9..c90c454 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -24,8 +24,7 @@ use std::future::Future;
 use std::io::{self, Read, Write};
 use std::pin::Pin;
 use std::task::{Context, Poll};
-use tokio::io::{AsyncRead, AsyncWrite};
-use std::mem::MaybeUninit;
+use tokio::io::{AsyncRead, AsyncWrite, ReadBuf};
 
 /// Asynchronously performs a client-side TLS handshake over the provided stream.
 pub async fn connect<S>(
@@ -99,10 +98,13 @@ where
     S: AsyncRead + Unpin,
 {
     fn read(&mut self, buf: &mut [u8]) -> io::Result<usize> {
-        match self.with_context(|ctx, stream| stream.poll_read(ctx, buf)) {
-            Poll::Ready(r) => r,
-            Poll::Pending => Err(io::Error::from(io::ErrorKind::WouldBlock)),
-        }
+        self.with_context(|ctx, stream| {
+            let mut buf = ReadBuf::new(buf);
+            match stream.poll_read(ctx, &mut buf)? {
+                Poll::Ready(()) => Ok(buf.filled().len()),
+                Poll::Pending => Err(io::Error::from(io::ErrorKind::WouldBlock)),
+            }
+        })
     }
 }
 
@@ -182,10 +184,7 @@ where
     ///
     /// The caller must ensure the pointer is valid.
     pub unsafe fn from_raw_parts(ssl: *mut ffi::SSL, stream: S) -> Self {
-        let stream = StreamWrapper {
-            stream,
-            context: 0,
-        };
+        let stream = StreamWrapper { stream, context: 0 };
         SslStream(ssl::SslStream::from_raw_parts(ssl, stream))
     }
 }
@@ -194,19 +193,18 @@ impl<S> AsyncRead for SslStream<S>
 where
     S: AsyncRead + AsyncWrite + Unpin,
 {
-    unsafe fn prepare_uninitialized_buffer(&self, _: &mut [MaybeUninit<u8>]) -> bool {
-        // Note that this does not forward to `S` because the buffer is
-        // unconditionally filled in by OpenSSL, not the actual object `S`.
-        // We're decrypting bytes from `S` into the buffer above!
-        false
-    }
-
     fn poll_read(
         mut self: Pin<&mut Self>,
         ctx: &mut Context<'_>,
-        buf: &mut [u8],
-    ) -> Poll<io::Result<usize>> {
-        self.with_context(ctx, |s| cvt(s.read(buf)))
+        buf: &mut ReadBuf<'_>,
+    ) -> Poll<io::Result<()>> {
+        self.with_context(ctx, |s| match cvt(s.read(buf.initialize_unfilled()))? {
+            Poll::Ready(nread) => {
+                buf.advance(nread);
+                Poll::Ready(Ok(()))
+            }
+            Poll::Pending => Poll::Pending,
+        })
     }
 }
 
diff --git a/tests/google.rs b/tests/google.rs
index 42b1f00..92060b8 100644
--- a/tests/google.rs
+++ b/tests/google.rs
@@ -33,7 +33,7 @@ async fn google() {
 
 #[tokio::test]
 async fn server() {
-    let mut listener = TcpListener::bind("127.0.0.1:0").await.unwrap();
+    let listener = TcpListener::bind("127.0.0.1:0").await.unwrap();
     let addr = listener.local_addr().unwrap();
 
     let server = async move {