diff --git a/src/proto/streams/send.rs b/src/proto/streams/send.rs
index ec201400..3735d13d 100644
--- a/src/proto/streams/send.rs
+++ b/src/proto/streams/send.rs
@@ -544,4 +544,14 @@ impl Send {
             true
         }
     }
+
+    pub(super) fn maybe_reset_next_stream_id(&mut self, id: StreamId) {
+        if let Ok(next_id) = self.next_stream_id {
+            // Peer::is_local_init should have been called beforehand
+            debug_assert_eq!(id.is_server_initiated(), next_id.is_server_initiated());
+            if id >= next_id {
+                self.next_stream_id = id.next_id();
+            }
+        }
+    }
 }
diff --git a/src/proto/streams/streams.rs b/src/proto/streams/streams.rs
index ac762c8f..4962db8d 100644
--- a/src/proto/streams/streams.rs
+++ b/src/proto/streams/streams.rs
@@ -865,6 +865,24 @@ impl Inner {
         let key = match self.store.find_entry(id) {
             Entry::Occupied(e) => e.key(),
             Entry::Vacant(e) => {
+                // Resetting a stream we don't know about? That could be OK...
+                //
+                // 1. As a server, we just received a request, but that request
+                //    was bad, so we're resetting before even accepting it.
+                //    This is totally fine.
+                //
+                // 2. The remote may have sent us a frame on new stream that
+                //    it's *not* supposed to have done, and thus, we don't know
+                //    the stream. In that case, sending a reset will "open" the
+                //    stream in our store. Maybe that should be a connection
+                //    error instead? At least for now, we need to update what
+                //    our vision of the next stream is.
+                if self.counts.peer().is_local_init(id) {
+                    // We normally would open this stream, so update our
+                    // next-send-id record.
+                    self.actions.send.maybe_reset_next_stream_id(id);
+                }
+
                 let stream = Stream::new(id, 0, 0);
 
                 e.insert(stream)
diff --git a/tests/h2-tests/tests/stream_states.rs b/tests/h2-tests/tests/stream_states.rs
index 91ef4939..f2b2efc1 100644
--- a/tests/h2-tests/tests/stream_states.rs
+++ b/tests/h2-tests/tests/stream_states.rs
@@ -1022,3 +1022,60 @@ async fn srv_window_update_on_lower_stream_id() {
     };
     join(srv, client).await;
 }
+
+// See https://github.com/hyperium/h2/issues/570
+#[tokio::test]
+async fn reset_new_stream_before_send() {
+    h2_support::trace_init!();
+    let (io, mut srv) = mock::new();
+
+    let srv = async move {
+        let settings = srv.assert_client_handshake().await;
+        assert_default_settings!(settings);
+        srv.recv_frame(
+            frames::headers(1)
+                .request("GET", "https://example.com/")
+                .eos(),
+        )
+        .await;
+        srv.send_frame(frames::headers(1).response(200).eos()).await;
+        // Send unexpected headers, that depends on itself, causing a framing error.
+        srv.send_bytes(&[
+            0, 0, 0x6,  // len
+            0x1,  // type (headers)
+            0x25, // flags (eos, eoh, pri)
+            0, 0, 0, 0x3, // stream id
+            0, 0, 0, 0x3,  // dependency
+            2,    // weight
+            0x88, // HPACK :status=200
+        ])
+        .await;
+        srv.recv_frame(frames::reset(3).protocol_error()).await;
+        srv.recv_frame(
+            frames::headers(5)
+                .request("GET", "https://example.com/")
+                .eos(),
+        )
+        .await;
+        srv.send_frame(frames::headers(5).response(200).eos()).await;
+    };
+
+    let client = async move {
+        let (mut client, mut conn) = client::handshake(io).await.expect("handshake");
+        let resp = conn
+            .drive(client.get("https://example.com/"))
+            .await
+            .unwrap();
+        assert_eq!(resp.status(), StatusCode::OK);
+
+        // req number 2
+        let resp = conn
+            .drive(client.get("https://example.com/"))
+            .await
+            .unwrap();
+        assert_eq!(resp.status(), StatusCode::OK);
+        conn.await.expect("client");
+    };
+
+    join(srv, client).await;
+}