diff --git a/docs/libraries/azure-core/rules/no-generic-types.md b/docs/libraries/azure-core/rules/no-generic-types.md
new file mode 100644
index 0000000000..11f0a8bff6
--- /dev/null
+++ b/docs/libraries/azure-core/rules/no-generic-types.md
@@ -0,0 +1,25 @@
+---
+title: "no-generic-types"
+---
+
+```text title="Full name"
+@azure-tools/typespec-azure-core/no-generic-types
+```
+
+Azure services should use types which specify the bit-width instead of generic types.
+
+#### ❌ Incorrect
+
+```tsp
+model Widget {
+  id: integer;
+}
+```
+
+#### ✅ Correct
+
+```tsp
+model Widget {
+  id: int32;
+}
+```
diff --git a/docs/libraries/azure-core/rules/use-standard-integer.md b/docs/libraries/azure-core/rules/use-standard-integer.md
deleted file mode 100644
index 6428c6cb6b..0000000000
--- a/docs/libraries/azure-core/rules/use-standard-integer.md
+++ /dev/null
@@ -1,25 +0,0 @@
----
-title: "use-standard-integer"
----
-
-```text title="Full name"
-@azure-tools/typespec-azure-core/use-standard-integer
-```
-
-Azure services favor the standard types int32 and int64 (or safeint) when generating code using Autorest.
-
-#### ❌ Incorrect
-
-```tsp
-model Widget {
-  id: int8;
-}
-```
-
-#### ✅ Correct
-
-```tsp
-model Widget {
-  id: int32;
-}
-```
diff --git a/packages/typespec-autorest/test/formats.test.ts b/packages/typespec-autorest/test/formats.test.ts
index 311d3eb124..a60635b72b 100644
--- a/packages/typespec-autorest/test/formats.test.ts
+++ b/packages/typespec-autorest/test/formats.test.ts
@@ -1,7 +1,7 @@
 import { expectDiagnosticEmpty, expectDiagnostics } from "@typespec/compiler/testing";
 import { deepStrictEqual } from "assert";
 import { describe, it } from "vitest";
-import { diagnoseOpenApiFor, emitOpenApiWithDiagnostics, openApiFor } from "./test-host.js";
+import { diagnoseOpenApiFor, openApiFor } from "./test-host.js";
 
 describe("typespec-autorest: format", () => {
   it("allows supported formats", async () => {
@@ -71,48 +71,4 @@ describe("typespec-autorest: format", () => {
     );
     expectDiagnosticEmpty(diagnostics);
   });
-
-  it("ensures certain scalars emit int32 and int64 formats", async () => {
-    const [res, _] = await emitOpenApiWithDiagnostics(
-      `
-      @service
-      namespace Test;
-
-      model Widget {
-        intA: int32;
-        intB: int64;
-        intC: safeint;
-        intD: numeric;
-        intE: integer;
-      }
-      `
-    );
-    const model = res.definitions!["Widget"]!;
-    deepStrictEqual(model, {
-      properties: {
-        intA: {
-          format: "int32",
-          type: "integer",
-        },
-        intB: {
-          format: "int64",
-          type: "integer",
-        },
-        intC: {
-          format: "int64",
-          type: "integer",
-        },
-        intD: {
-          format: "int64",
-          type: "integer",
-        },
-        intE: {
-          format: "int64",
-          type: "integer",
-        },
-      },
-      required: ["intA", "intB", "intC", "intD", "intE"],
-      type: "object",
-    });
-  });
 });
diff --git a/packages/typespec-azure-core/src/linter.ts b/packages/typespec-azure-core/src/linter.ts
index 05d946649d..b07e84844f 100644
--- a/packages/typespec-azure-core/src/linter.ts
+++ b/packages/typespec-azure-core/src/linter.ts
@@ -13,6 +13,7 @@ import { noEnumRule } from "./rules/no-enum.js";
 import { noErrorStatusCodesRule } from "./rules/no-error-status-codes.js";
 import { noExplicitRoutesResourceOps } from "./rules/no-explicit-routes-resource-ops.js";
 import { noFixedEnumDiscriminatorRule } from "./rules/no-fixed-enum-discriminator.js";
+import { noGenericTypesRule } from "./rules/no-generic-types.js";
 import { noNullableRule } from "./rules/no-nullable.js";
 import { noOffsetDateTimeRule } from "./rules/no-offsetdatetime.js";
 import { operationIdRule } from "./rules/no-operation-id.js";
@@ -32,7 +33,6 @@ import { requireKeyVisibility } from "./rules/require-key-visibility.js";
 import { responseSchemaMultiStatusCodeRule } from "./rules/response-schema-multi-status-code.js";
 import { rpcOperationRequestBodyRule } from "./rules/rpc-operation-request-body.js";
 import { spreadDiscriminatedModelRule } from "./rules/spread-discriminated-model.js";
-import { useStandardInteger } from "./rules/use-standard-integer.js";
 import { useStandardNames } from "./rules/use-standard-names.js";
 import { useStandardOperations } from "./rules/use-standard-ops.js";
 
@@ -52,6 +52,7 @@ const rules = [
   noExplicitRoutesResourceOps,
   noFixedEnumDiscriminatorRule,
   nonBreakingVersioningRule,
+  noGenericTypesRule,
   noNullableRule,
   noOffsetDateTimeRule,
   noResponseBodyRule,
@@ -69,7 +70,6 @@ const rules = [
   responseSchemaMultiStatusCodeRule,
   rpcOperationRequestBodyRule,
   spreadDiscriminatedModelRule,
-  useStandardInteger,
   useStandardNames,
   useStandardOperations,
 ];
diff --git a/packages/typespec-azure-core/src/rules/no-generic-types.ts b/packages/typespec-azure-core/src/rules/no-generic-types.ts
new file mode 100644
index 0000000000..c88ff7330d
--- /dev/null
+++ b/packages/typespec-azure-core/src/rules/no-generic-types.ts
@@ -0,0 +1,38 @@
+import { Model, createRule, paramMessage } from "@typespec/compiler";
+
+const disallowList = new Set(["integer", "numeric", "float", "decimal"]);
+const alternatives = new Map([
+  ["integer", "int32"],
+  ["numeric", "int32"],
+  ["float", "float32"],
+  ["decimal", "float32"],
+]);
+
+export const noGenericTypesRule = createRule({
+  name: "no-generic-types",
+  description: "Don't use generic types. Use more specific types instead.",
+  severity: "warning",
+  url: "https://azure.github.io/typespec-azure/docs/libraries/azure-core/rules/no-generic-types",
+  messages: {
+    default: paramMessage`Don't use generic type '${"name"}'. Use a more specific type that specifies the bit size, such as '${"alternative"}' instead.`,
+  },
+  create(context) {
+    return {
+      model: (model: Model) => {
+        for (const [_, prop] of model.properties) {
+          if (prop.type.kind === "Scalar") {
+            if (disallowList.has(prop.type.name)) {
+              context.reportDiagnostic({
+                target: prop.type,
+                format: {
+                  name: prop.type.name,
+                  alternative: alternatives.get(prop.type.name)!,
+                },
+              });
+            }
+          }
+        }
+      },
+    };
+  },
+});
diff --git a/packages/typespec-azure-core/src/rules/use-standard-integer.ts b/packages/typespec-azure-core/src/rules/use-standard-integer.ts
deleted file mode 100644
index 00e7724a37..0000000000
--- a/packages/typespec-azure-core/src/rules/use-standard-integer.ts
+++ /dev/null
@@ -1,35 +0,0 @@
-import { Model, createRule } from "@typespec/compiler";
-
-export const useStandardInteger = createRule({
-  name: "use-standard-integer",
-  description: "Use only types that map to int32 or int64.",
-  severity: "warning",
-  url: "https://azure.github.io/typespec-azure/docs/libraries/azure-core/rules/use-standard-integer",
-  messages: {
-    default: "Recommended integer types are 'int32', 'int64' or 'safeint'.",
-  },
-  create(context) {
-    return {
-      model: (model: Model) => {
-        const nonRecommendedInts = [
-          "int64",
-          "int8",
-          "int16",
-          "uint8",
-          "uint16",
-          "uint32",
-          "uint64",
-        ];
-        for (const [_, prop] of model.properties) {
-          if (prop.type.kind === "Scalar") {
-            if (nonRecommendedInts.includes(prop.type.name)) {
-              context.reportDiagnostic({
-                target: prop.type,
-              });
-            }
-          }
-        }
-      },
-    };
-  },
-});
diff --git a/packages/typespec-azure-core/test/rules/use-standard-integer.test.ts b/packages/typespec-azure-core/test/rules/no-generic-types.test.ts
similarity index 91%
rename from packages/typespec-azure-core/test/rules/use-standard-integer.test.ts
rename to packages/typespec-azure-core/test/rules/no-generic-types.test.ts
index 5b74156606..5e3213f0fa 100644
--- a/packages/typespec-azure-core/test/rules/use-standard-integer.test.ts
+++ b/packages/typespec-azure-core/test/rules/no-generic-types.test.ts
@@ -4,7 +4,7 @@ import {
   createLinterRuleTester,
 } from "@typespec/compiler/testing";
 import { beforeEach, it } from "vitest";
-import { useStandardInteger } from "../../src/rules/use-standard-integer.js";
+import { noGenericTypesRule } from "../../src/rules/no-generic-types.js";
 import { createAzureCoreTestRunner } from "../test-host.js";
 
 let runner: BasicTestRunner;
@@ -12,7 +12,7 @@ let tester: LinterRuleTester;
 
 beforeEach(async () => {
   runner = await createAzureCoreTestRunner({ omitServiceNamespace: true });
-  tester = createLinterRuleTester(runner, useStandardInteger, "@azure-tools/typespec-azure-core");
+  tester = createLinterRuleTester(runner, noGenericTypesRule, "@azure-tools/typespec-azure-core");
 });
 
 it("emits a warning diagnostic for non-standard integer types", async () => {