diff --git a/apps/server/src/mcp/advertisedJsonSchema.test.ts b/apps/server/src/mcp/advertisedJsonSchema.test.ts
index 09a90556a9dd0..3a96fe299b144 100644
--- a/apps/server/src/mcp/advertisedJsonSchema.test.ts
+++ b/apps/server/src/mcp/advertisedJsonSchema.test.ts
@@ -3,14 +3,18 @@ import * as Schema from "effect/Schema";
 import { Tool } from "effect/ai";
 
 import { advertisedJsonSchema } from "./advertisedJsonSchema.ts";
+import { ThreadToolkit } from "./toolkits/thread/tools.ts";
 
-it("drops JSON noise, merges tagged unions, and keeps null where it is required", () => {
+it("drops JSON noise, merges tagged unions, and keeps null where it is required or described", () => {
   const Every = Schema.Struct({ ms: Schema.Int });
   const tool = Tool.make("example", {
     parameters: Schema.Struct({
       threadId: Schema.optional(Schema.NullOr(Schema.String)),
       beforeRunId: Schema.NullOr(Schema.String),
       limit: Schema.optional(Schema.Int),
+      after: Schema.optional(
+        Schema.Union([Schema.String, Schema.Null.annotate({ description: "Last." })]),
+      ),
       every: Schema.Union([Every, Schema.fromJsonString(Every)]),
       target: Schema.optional(
         Schema.NullOr(
@@ -29,6 +33,7 @@ it("drops JSON noise, merges tagged unions, and keeps null where it is required"
       threadId: { type: "string" },
       beforeRunId: { anyOf: [{ type: "string" }, { type: "null" }] },
       limit: { type: "integer" },
+      after: { anyOf: [{ type: "string" }, { type: "null", description: "Last." }] },
       every: { type: "object", properties: { ms: { type: "integer" } }, required: ["ms"] },
       target: {
         type: "object",
@@ -43,3 +48,9 @@ it("drops JSON noise, merges tagged unions, and keeps null where it is required"
     required: ["beforeRunId", "every"],
   });
 });
+
+it("advertises null for t3_queue's beforeRunId, which moves a message to the end", () => {
+  expect(advertisedJsonSchema(ThreadToolkit.tools.t3_queue)).toMatchObject({
+    properties: { beforeRunId: { anyOf: [{ type: "string" }, { type: "null" }] } },
+  });
+});
diff --git a/apps/server/src/mcp/advertisedJsonSchema.ts b/apps/server/src/mcp/advertisedJsonSchema.ts
index 10001307f2d6c..8c3a59d3c4241 100644
--- a/apps/server/src/mcp/advertisedJsonSchema.ts
+++ b/apps/server/src/mcp/advertisedJsonSchema.ts
@@ -97,10 +97,10 @@ const compact = (schema: Json, optional: boolean): Json => {
 };
 
 /**
- * The input schema T3 advertises for a tool. Drops JSON noise that every thread pays for:
- * `additionalProperties: true`, safe-integer bounds, nested `anyOf`, JSON-string fallbacks, and
- * the `null` branch of optional properties. A tagged union of objects becomes one object.
- * Decoding still uses the full schema, so each tag's own required fields still apply.
+ * The input schema T3 advertises for a tool, without JSON noise every thread pays for. A tagged
+ * union of objects becomes one object; decoding still uses the full schema. An optional property
+ * loses its bare `null` branch: where `null` means more than "omitted", describe it
+ * (`Schema.Null.annotate({ description })`) and it stays.
  */
 export const advertisedJsonSchema = (tool: Tool.Any) =>
   compact(Tool.getJsonSchema(tool), false) as ReturnType<typeof Tool.getJsonSchema>;
diff --git a/apps/server/src/mcp/toolkits/thread/tools.ts b/apps/server/src/mcp/toolkits/thread/tools.ts
index 4c59ea4f2028f..c2a352b9b4b95 100644
--- a/apps/server/src/mcp/toolkits/thread/tools.ts
+++ b/apps/server/src/mcp/toolkits/thread/tools.ts
@@ -96,7 +96,9 @@ const QueueTool = Tool.make("t3_queue", {
     threadId: Schema.optional(ThreadId),
     queuedRunId: Schema.optional(RunId),
     text: Schema.optional(Schema.String.check(Schema.isMaxLength(100000))),
-    beforeRunId: Schema.optional(Schema.NullOr(RunId)),
+    beforeRunId: Schema.optional(
+      Schema.Union([RunId, Schema.Null.annotate({ description: "To the end." })]),
+    ),
     targetRunId: Schema.optional(RunId),
     cursor: Schema.optional(NonNegativeInt),
     limit: Schema.optional(Schema.Int.check(Schema.isBetween({ minimum: 1, maximum: 100 }))),
diff --git a/apps/server/src/provider/agentContextBudget.json b/apps/server/src/provider/agentContextBudget.json
index e7901a8656ebe..ff951d8d97ffe 100644
--- a/apps/server/src/provider/agentContextBudget.json
+++ b/apps/server/src/provider/agentContextBudget.json
@@ -1,5 +1,5 @@
 {
   "claudeSystemAppendBytes": 5594,
   "codexAdditionalContextBytes": 7324,
-  "mcpToolListJsonBytes": 48094
+  "mcpToolListJsonBytes": 48150
 }