diff --git a/codex-rs/mcp-server/src/codex_tool_config.rs b/codex-rs/mcp-server/src/codex_tool_config.rs
index 16d38da45e7..26fdc073206 100644
--- a/codex-rs/mcp-server/src/codex_tool_config.rs
+++ b/codex-rs/mcp-server/src/codex_tool_config.rs
@@ -21,7 +21,7 @@ pub struct CodexToolCallParam {
     /// The *initial user prompt* to start the Codex conversation.
     pub prompt: String,
 
-    /// Optional override for the model name (e.g. "o3", "o4-mini").
+    /// Optional override for the model name (e.g. 'gpt-5.2', 'gpt-5.2-codex').
     #[serde(default, skip_serializing_if = "Option::is_none")]
     pub model: Option<String>,
 
@@ -245,11 +245,8 @@ mod tests {
         let tool = create_tool_for_codex_tool_call_param();
         let tool_json = serde_json::to_value(&tool).expect("tool serializes");
         let expected_tool_json = serde_json::json!({
-          "name": "codex",
-          "title": "Codex",
           "description": "Run a Codex session. Accepts configuration parameters matching the Codex Config struct.",
           "inputSchema": {
-            "type": "object",
             "properties": {
               "approval-policy": {
                 "description": "Approval policy for shell commands generated by the model: `untrusted`, `on-failure`, `on-request`, `never`.",
@@ -261,26 +258,29 @@ mod tests {
                 ],
                 "type": "string"
               },
-              "sandbox": {
-                "description": "Sandbox mode: `read-only`, `workspace-write`, or `danger-full-access`.",
-                "enum": [
-                  "read-only",
-                  "workspace-write",
-                  "danger-full-access"
-                ],
+              "base-instructions": {
+                "description": "The set of instructions to use instead of the default ones.",
+                "type": "string"
+              },
+              "compact-prompt": {
+                "description": "Prompt used when compacting the conversation.",
                 "type": "string"
               },
               "config": {
-                "description": "Individual config settings that will override what is in CODEX_HOME/config.toml.",
                 "additionalProperties": true,
+                "description": "Individual config settings that will override what is in CODEX_HOME/config.toml.",
                 "type": "object"
               },
               "cwd": {
                 "description": "Working directory for the session. If relative, it is resolved against the server process's current working directory.",
                 "type": "string"
               },
+              "developer-instructions": {
+                "description": "Developer instructions that should be injected as a developer role message.",
+                "type": "string"
+              },
               "model": {
-                "description": "Optional override for the model name (e.g. \"o3\", \"o4-mini\").",
+                "description": "Optional override for the model name (e.g. 'gpt-5.2', 'gpt-5.2-codex').",
                 "type": "string"
               },
               "profile": {
@@ -291,23 +291,23 @@ mod tests {
                 "description": "The *initial user prompt* to start the Codex conversation.",
                 "type": "string"
               },
-              "base-instructions": {
-                "description": "The set of instructions to use instead of the default ones.",
-                "type": "string"
-              },
-              "developer-instructions": {
-                "description": "Developer instructions that should be injected as a developer role message.",
-                "type": "string"
-              },
-              "compact-prompt": {
-                "description": "Prompt used when compacting the conversation.",
+              "sandbox": {
+                "description": "Sandbox mode: `read-only`, `workspace-write`, or `danger-full-access`.",
+                "enum": [
+                  "read-only",
+                  "workspace-write",
+                  "danger-full-access"
+                ],
                 "type": "string"
-              },
+              }
             },
             "required": [
               "prompt"
-            ]
-          }
+            ],
+            "type": "object"
+          },
+          "name": "codex",
+          "title": "Codex"
         });
         assert_eq!(expected_tool_json, tool_json);
     }