diff --git a/src/core.ts b/src/core.ts
index b00ebe99..d5a3900c 100644
--- a/src/core.ts
+++ b/src/core.ts
@@ -417,14 +417,17 @@ export abstract class APIClient {
 
     if (!response.ok) {
       if (retriesRemaining && this.shouldRetry(response)) {
+        const retryMessage = `retrying, ${retriesRemaining} attempts remaining`;
+        debug(`response (error; ${retryMessage})`, response.status, url, responseHeaders);
         return this.retryRequest(options, retriesRemaining, responseHeaders);
       }
 
       const errText = await response.text().catch((e) => castToError(e).message);
       const errJSON = safeJSON(errText);
       const errMessage = errJSON ? undefined : errText;
+      const retryMessage = retriesRemaining ? `(error; no more retries left)` : `(error; not retryable)`;
 
-      debug('response', response.status, url, responseHeaders, errMessage);
+      debug(`response (error; ${retryMessage})`, response.status, url, responseHeaders, errMessage);
 
       const err = this.makeStatusError(response.status, errJSON, errMessage, responseHeaders);
       throw err;
@@ -529,11 +532,21 @@ export abstract class APIClient {
     retriesRemaining: number,
     responseHeaders?: Headers | undefined,
   ): Promise<APIResponseProps> {
-    // About the Retry-After header: https://developer.mozilla.org/en-US/docs/Web/HTTP/Headers/Retry-After
     let timeoutMillis: number | undefined;
+
+    // Note the `retry-after-ms` header may not be standard, but is a good idea and we'd like proactive support for it.
+    const retryAfterMillisHeader = responseHeaders?.['retry-after-ms'];
+    if (retryAfterMillisHeader) {
+      const timeoutMs = parseFloat(retryAfterMillisHeader);
+      if (!Number.isNaN(timeoutMs)) {
+        timeoutMillis = timeoutMs;
+      }
+    }
+
+    // About the Retry-After header: https://developer.mozilla.org/en-US/docs/Web/HTTP/Headers/Retry-After
     const retryAfterHeader = responseHeaders?.['retry-after'];
-    if (retryAfterHeader) {
-      const timeoutSeconds = parseInt(retryAfterHeader);
+    if (retryAfterHeader && !timeoutMillis) {
+      const timeoutSeconds = parseFloat(retryAfterHeader);
       if (!Number.isNaN(timeoutSeconds)) {
         timeoutMillis = timeoutSeconds * 1000;
       } else {
@@ -543,12 +556,7 @@ export abstract class APIClient {
 
     // If the API asks us to wait a certain amount of time (and it's a reasonable amount),
     // just do what it says, but otherwise calculate a default
-    if (
-      !timeoutMillis ||
-      !Number.isInteger(timeoutMillis) ||
-      timeoutMillis <= 0 ||
-      timeoutMillis > 60 * 1000
-    ) {
+    if (!(timeoutMillis && 0 <= timeoutMillis && timeoutMillis < 60 * 1000)) {
       const maxRetries = options.maxRetries ?? this.maxRetries;
       timeoutMillis = this.calculateDefaultRetryTimeoutMillis(retriesRemaining, maxRetries);
     }
diff --git a/tests/index.test.ts b/tests/index.test.ts
index 67e94353..5ebbeef3 100644
--- a/tests/index.test.ts
+++ b/tests/index.test.ts
@@ -223,17 +223,18 @@ describe('request building', () => {
 });
 
 describe('retries', () => {
-  test('single retry', async () => {
+  test('retry on timeout', async () => {
     let count = 0;
     const testFetch = async (url: RequestInfo, { signal }: RequestInit = {}): Promise<Response> => {
-      if (!count++)
+      if (count++ === 0) {
         return new Promise(
           (resolve, reject) => signal?.addEventListener('abort', () => reject(new Error('timed out'))),
         );
+      }
       return new Response(JSON.stringify({ a: 1 }), { headers: { 'Content-Type': 'application/json' } });
     };
 
-    const client = new Anthropic({ apiKey: 'my-anthropic-api-key', timeout: 2000, fetch: testFetch });
+    const client = new Anthropic({ apiKey: 'my-anthropic-api-key', timeout: 10, fetch: testFetch });
 
     expect(await client.request({ path: '/foo', method: 'get' })).toEqual({ a: 1 });
     expect(count).toEqual(2);
@@ -244,5 +245,59 @@ describe('retries', () => {
         .then((r) => r.text()),
     ).toEqual(JSON.stringify({ a: 1 }));
     expect(count).toEqual(3);
-  }, 10000);
+  });
+
+  test('retry on 429 with retry-after', async () => {
+    let count = 0;
+    const testFetch = async (url: RequestInfo, { signal }: RequestInit = {}): Promise<Response> => {
+      if (count++ === 0) {
+        return new Response(undefined, {
+          status: 429,
+          headers: {
+            'Retry-After': '0.1',
+          },
+        });
+      }
+      return new Response(JSON.stringify({ a: 1 }), { headers: { 'Content-Type': 'application/json' } });
+    };
+
+    const client = new Anthropic({ apiKey: 'my-anthropic-api-key', fetch: testFetch });
+
+    expect(await client.request({ path: '/foo', method: 'get' })).toEqual({ a: 1 });
+    expect(count).toEqual(2);
+    expect(
+      await client
+        .request({ path: '/foo', method: 'get' })
+        .asResponse()
+        .then((r) => r.text()),
+    ).toEqual(JSON.stringify({ a: 1 }));
+    expect(count).toEqual(3);
+  });
+
+  test('retry on 429 with retry-after-ms', async () => {
+    let count = 0;
+    const testFetch = async (url: RequestInfo, { signal }: RequestInit = {}): Promise<Response> => {
+      if (count++ === 0) {
+        return new Response(undefined, {
+          status: 429,
+          headers: {
+            'Retry-After-Ms': '10',
+          },
+        });
+      }
+      return new Response(JSON.stringify({ a: 1 }), { headers: { 'Content-Type': 'application/json' } });
+    };
+
+    const client = new Anthropic({ apiKey: 'my-anthropic-api-key', fetch: testFetch });
+
+    expect(await client.request({ path: '/foo', method: 'get' })).toEqual({ a: 1 });
+    expect(count).toEqual(2);
+    expect(
+      await client
+        .request({ path: '/foo', method: 'get' })
+        .asResponse()
+        .then((r) => r.text()),
+    ).toEqual(JSON.stringify({ a: 1 }));
+    expect(count).toEqual(3);
+  });
 });