diff --git a/src/s2_sdk/_client.py b/src/s2_sdk/_client.py
index 7150bbc..1baf9cf 100644
--- a/src/s2_sdk/_client.py
+++ b/src/s2_sdk/_client.py
@@ -376,15 +376,26 @@ async def checkout(self, base_url: str) -> _Checkout:
             except asyncio.TimeoutError:
                 pass  # Proceed with h2 defaults
 
+            if conn._goaway_received:
+                await conn.close()
+                raise ConnectError(
+                    f"Server sent GOAWAY on connection to {host}:{port} before "
+                    "an HTTP/2 request stream could be reserved"
+                )
+
             if conn._recv_dead:
                 await conn.close()
                 raise ConnectError(
-                    f"Connection to {host}:{port} closed before HTTP/2 SETTINGS"
+                    f"HTTP/2 receive loop for connection to {host}:{port} "
+                    "terminated before a request stream could be reserved"
                 )
 
             if conn._settings_received.is_set() and conn.max_concurrent_streams <= 0:
                 await conn.close()
-                raise ProtocolError("Connection has no available stream capacity")
+                raise ConnectError(
+                    f"Server's initial HTTP/2 SETTINGS for {host}:{port} "
+                    "advertised zero concurrent streams"
+                )
 
             pc = await self._add_connection(base_url, conn)
             state = pc._conn.reserve_stream()
diff --git a/tests/test_client.py b/tests/test_client.py
index 7286f21..5641b1c 100644
--- a/tests/test_client.py
+++ b/tests/test_client.py
@@ -13,8 +13,8 @@
     _StreamState,
 )
 from s2_sdk._exceptions import (
+    ConnectError,
     ConnectionClosedError,
-    ProtocolError,
     ReadTimeoutError,
     S2ClientError,
     S2ServerError,
@@ -37,6 +37,7 @@ def _mock_connection(
     conn.close = AsyncMock()
     conn._streams = {}
     conn._pending_streams = {}
+    conn._goaway_received = False
     conn._recv_dead = False
     conn._settings_received = asyncio.Event()
     conn._settings_received.set()
@@ -176,7 +177,7 @@ async def test_new_connection_with_zero_stream_capacity_raises(pool: ConnectionP
         conn = _mock_connection(max_concurrent_streams=0)
         MockConn.return_value = conn
 
-        with pytest.raises(ProtocolError, match="no available stream capacity"):
+        with pytest.raises(ConnectError, match="zero concurrent streams"):
             await pool.checkout("https://example.com")
 
         conn.close.assert_awaited_once()