diff --git a/openssl/src/ssl/bio.rs b/openssl/src/ssl/bio.rs
index 1009c0bc..ef63d146 100644
--- a/openssl/src/ssl/bio.rs
+++ b/openssl/src/ssl/bio.rs
@@ -95,7 +95,7 @@ unsafe extern "C" fn bwrite<S: Write>(bio: *mut BIO, buf: *const c_char, len: c_
     match state.stream.write(buf) {
         Ok(len) => len as c_int,
         Err(err) => {
-            if err.kind() == io::ErrorKind::WouldBlock {
+            if retriable_error(&err) {
                 BIO_set_retry_write(bio);
             }
             state.error = Some(err);
@@ -112,7 +112,7 @@ unsafe extern "C" fn bread<S: Read>(bio: *mut BIO, buf: *mut c_char, len: c_int)
     match state.stream.read(buf) {
         Ok(len) => len as c_int,
         Err(err) => {
-            if err.kind() == io::ErrorKind::WouldBlock {
+            if retriable_error(&err) {
                 BIO_set_retry_read(bio);
             }
             state.error = Some(err);
@@ -121,6 +121,13 @@ unsafe extern "C" fn bread<S: Read>(bio: *mut BIO, buf: *mut c_char, len: c_int)
     }
 }
 
+fn retriable_error(err: &io::Error) -> bool {
+    match err.kind() {
+        io::ErrorKind::WouldBlock | io::ErrorKind::NotConnected => true,
+        _ => false
+    }
+}
+
 unsafe extern "C" fn bputs<S: Write>(bio: *mut BIO, s: *const c_char) -> c_int {
     bwrite::<S>(bio, s, strlen(s) as c_int)
 }
diff --git a/openssl/src/ssl/mod.rs b/openssl/src/ssl/mod.rs
index 183cf19d..d529347f 100644
--- a/openssl/src/ssl/mod.rs
+++ b/openssl/src/ssl/mod.rs
@@ -1070,16 +1070,10 @@ impl<S: Read + Write> SslStream<S> {
         if ret > 0 {
             Ok(stream)
         } else {
-            match stream.make_old_error(ret) {
-                SslError::StreamError(e) => {
-                    // This is fine - nonblocking sockets will finish the handshake in read/write
-                    if e.kind() == io::ErrorKind::WouldBlock {
-                        Ok(stream)
-                    } else {
-                        Err(SslError::StreamError(e))
-                    }
-                }
-                e => Err(e),
+            match stream.make_error(ret) {
+                // This is fine - nonblocking sockets will finish the handshake in read/write
+                Error::WantRead(..) | Error::WantWrite(..) => Ok(stream),
+                _ => Err(stream.make_old_error(ret)),
             }
         }
     }
@@ -1092,16 +1086,10 @@ impl<S: Read + Write> SslStream<S> {
         if ret > 0 {
             Ok(stream)
         } else {
-            match stream.make_old_error(ret) {
-                SslError::StreamError(e) => {
-                    // This is fine - nonblocking sockets will finish the handshake in read/write
-                    if e.kind() == io::ErrorKind::WouldBlock {
-                        Ok(stream)
-                    } else {
-                        Err(SslError::StreamError(e))
-                    }
-                }
-                e => Err(e),
+            match stream.make_error(ret) {
+                // This is fine - nonblocking sockets will finish the handshake in read/write
+                Error::WantRead(..) | Error::WantWrite(..) => Ok(stream),
+                _ => Err(stream.make_old_error(ret)),
             }
         }
     }