diff --git a/codex-rs/codex-api/src/endpoint/realtime_websocket/mode_v2.rs b/codex-rs/codex-api/src/endpoint/realtime_websocket/mode_v2.rs
index 12f164c15d..7a85ce6190 100644
--- a/codex-rs/codex-api/src/endpoint/realtime_websocket/mode_v2.rs
+++ b/codex-rs/codex-api/src/endpoint/realtime_websocket/mode_v2.rs
@@ -106,6 +106,10 @@ pub(super) fn append_query_params(
     query_params: Option<&HashMap<String, String>>,
     model: Option<&str>,
 ) {
+    if model.is_none() && query_params.is_none_or(HashMap::is_empty) {
+        return;
+    }
+
     let mut query = url.query_pairs_mut();
     if let Some(model) = model {
         query.append_pair("model", model);
diff --git a/codex-rs/core/config.schema.json b/codex-rs/core/config.schema.json
index 19fafb40ff..af8f979824 100644
--- a/codex-rs/core/config.schema.json
+++ b/codex-rs/core/config.schema.json
@@ -398,10 +398,10 @@
             "prevent_idle_sleep": {
               "type": "boolean"
             },
-            "realtime_v2": {
+            "realtime_conversation": {
               "type": "boolean"
             },
-            "realtime_conversation": {
+            "realtime_v2": {
               "type": "boolean"
             },
             "remote_models": {
@@ -1792,10 +1792,10 @@
         "prevent_idle_sleep": {
           "type": "boolean"
         },
-        "realtime_v2": {
+        "realtime_conversation": {
           "type": "boolean"
         },
-        "realtime_conversation": {
+        "realtime_v2": {
           "type": "boolean"
         },
         "remote_models": {