diff --git a/packages/workbox-core/_private.mjs b/packages/workbox-core/_private.mjs
index 3e19cdd78..da1db70b9 100644
--- a/packages/workbox-core/_private.mjs
+++ b/packages/workbox-core/_private.mjs
@@ -7,26 +7,30 @@
 */
 
 // We either expose defaults or we expose every named export.
-import {DBWrapper} from './_private/DBWrapper.mjs';
-import {deleteDatabase} from './_private/deleteDatabase.mjs';
-import {WorkboxError} from './_private/WorkboxError.mjs';
 import {assert} from './_private/assert.mjs';
 import {cacheNames} from './_private/cacheNames.mjs';
 import {cacheWrapper} from './_private/cacheWrapper.mjs';
+import {DBWrapper} from './_private/DBWrapper.mjs';
+import {Deferred} from './_private/Deferred.mjs';
+import {deleteDatabase} from './_private/deleteDatabase.mjs';
+import {executeQuotaErrorCallbacks} from './_private/executeQuotaErrorCallbacks.mjs';
 import {fetchWrapper} from './_private/fetchWrapper.mjs';
 import {getFriendlyURL} from './_private/getFriendlyURL.mjs';
 import {logger} from './_private/logger.mjs';
+import {WorkboxError} from './_private/WorkboxError.mjs';
 
 import './_version.mjs';
 
 export {
-  DBWrapper,
-  deleteDatabase,
-  WorkboxError,
   assert,
   cacheNames,
   cacheWrapper,
+  DBWrapper,
+  Deferred,
+  deleteDatabase,
+  executeQuotaErrorCallbacks,
   fetchWrapper,
   getFriendlyURL,
   logger,
+  WorkboxError,
 };
diff --git a/packages/workbox-core/_private/cacheWrapper.mjs b/packages/workbox-core/_private/cacheWrapper.mjs
index 3e92ad006..e7df56b8d 100644
--- a/packages/workbox-core/_private/cacheWrapper.mjs
+++ b/packages/workbox-core/_private/cacheWrapper.mjs
@@ -6,13 +6,13 @@
   https://opensource.org/licenses/MIT.
 */
 
-import {pluginEvents} from '../models/pluginEvents.mjs';
-import {pluginUtils} from '../utils/pluginUtils.mjs';
 import {WorkboxError} from './WorkboxError.mjs';
 import {assert} from './assert.mjs';
-import {executeQuotaErrorCallbacks} from './quota.mjs';
 import {getFriendlyURL} from './getFriendlyURL.mjs';
 import {logger} from './logger.mjs';
+import {executeQuotaErrorCallbacks} from './executeQuotaErrorCallbacks.mjs';
+import {pluginEvents} from '../models/pluginEvents.mjs';
+import {pluginUtils} from '../utils/pluginUtils.mjs';
 import '../_version.mjs';
 
 
diff --git a/packages/workbox-core/_private/checkSWFileCacheHeaders.mjs b/packages/workbox-core/_private/checkSWFileCacheHeaders.mjs
deleted file mode 100644
index 42709a577..000000000
--- a/packages/workbox-core/_private/checkSWFileCacheHeaders.mjs
+++ /dev/null
@@ -1,80 +0,0 @@
-/*
-  Copyright 2018 Google LLC
-
-  Use of this source code is governed by an MIT-style
-  license that can be found in the LICENSE file or at
-  https://opensource.org/licenses/MIT.
-*/
-
-import {logger} from './logger.mjs';
-import '../_version.mjs';
-
-/**
- * Logs a warning to the user recommending changing
- * to max-age=0 or no-cache.
- *
- * @param {string} cacheControlHeader
- *
- * @private
- */
-function showWarning(cacheControlHeader) {
-  const docsURL = 'https://developers.google.com/web/tools/workbox/guides/service-worker-checklist#cache-control_of_your_service_worker_file';
-  logger.warn(`You are setting a 'cache-control' header of ` +
-    `'${cacheControlHeader}' on your service worker file. This should be ` +
-    `set to 'max-age=0' or 'no-cache' to ensure the latest service worker ` +
-    `is served to your users. Learn more here: ${docsURL}`
-  );
-}
-
-/**
- * Checks for cache-control header on SW file and
- * warns the developer if it exists with a value
- * other than max-age=0 or no-cache.
- *
- * @return {Promise}
- * @private
- */
-function checkSWFileCacheHeaders() {
-  // This is wrapped as an iife to allow async/await while making
-  //  rollup exclude it in builds.
-  return (async () => {
-    try {
-      const swFile = self.location.href;
-      const response = await fetch(swFile);
-      if (!response.ok) {
-        // Response failed so nothing we can check;
-        return;
-      }
-
-      if (!response.headers.has('cache-control')) {
-        // No cache control header.
-        return;
-      }
-
-      const cacheControlHeader = response.headers.get('cache-control');
-      const maxAgeResult = /max-age\s*=\s*(\d*)/g.exec(cacheControlHeader);
-      if (maxAgeResult) {
-        if (parseInt(maxAgeResult[1], 10) === 0) {
-          return;
-        }
-      }
-
-      if (cacheControlHeader.indexOf('no-cache') !== -1) {
-        return;
-      }
-
-      if (cacheControlHeader.indexOf('no-store') !== -1) {
-        return;
-      }
-
-      showWarning(cacheControlHeader);
-    } catch (err) {
-      // NOOP
-    }
-  })();
-}
-
-const finalCheckSWFileCacheHeaders =
-  process.env.NODE_ENV === 'production' ? null : checkSWFileCacheHeaders;
-
-export {finalCheckSWFileCacheHeaders as checkSWFileCacheHeaders};
diff --git a/packages/workbox-core/_private/executeQuotaErrorCallbacks.mjs b/packages/workbox-core/_private/executeQuotaErrorCallbacks.mjs
new file mode 100644
index 000000000..3653d7a61
--- /dev/null
+++ b/packages/workbox-core/_private/executeQuotaErrorCallbacks.mjs
@@ -0,0 +1,39 @@
+/*
+  Copyright 2018 Google LLC
+
+  Use of this source code is governed by an MIT-style
+  license that can be found in the LICENSE file or at
+  https://opensource.org/licenses/MIT.
+*/
+
+import {logger} from '../_private/logger.mjs';
+import {quotaErrorCallbacks} from '../models/quotaErrorCallbacks.mjs';
+import '../_version.mjs';
+
+
+/**
+ * Runs all of the callback functions, one at a time sequentially, in the order
+ * in which they were registered.
+ *
+ * @memberof workbox.core
+ * @private
+ */
+async function executeQuotaErrorCallbacks() {
+  if (process.env.NODE_ENV !== 'production') {
+    logger.log(`About to run ${quotaErrorCallbacks.size} ` +
+        `callbacks to clean up caches.`);
+  }
+
+  for (const callback of quotaErrorCallbacks) {
+    await callback();
+    if (process.env.NODE_ENV !== 'production') {
+      logger.log(callback, 'is complete.');
+    }
+  }
+
+  if (process.env.NODE_ENV !== 'production') {
+    logger.log('Finished running callbacks.');
+  }
+}
+
+export {executeQuotaErrorCallbacks};
diff --git a/packages/workbox-core/_private/quota.mjs b/packages/workbox-core/_private/quota.mjs
deleted file mode 100644
index 78037acc5..000000000
--- a/packages/workbox-core/_private/quota.mjs
+++ /dev/null
@@ -1,66 +0,0 @@
-/*
-  Copyright 2018 Google LLC
-
-  Use of this source code is governed by an MIT-style
-  license that can be found in the LICENSE file or at
-  https://opensource.org/licenses/MIT.
-*/
-
-import {logger} from './logger.mjs';
-import {assert} from './assert.mjs';
-
-import '../_version.mjs';
-
-const callbacks = new Set();
-
-/**
- * Adds a function to the set of callbacks that will be executed when there's
- * a quota error.
- *
- * @param {Function} callback
- * @memberof workbox.core
- */
-function registerQuotaErrorCallback(callback) {
-  if (process.env.NODE_ENV !== 'production') {
-    assert.isType(callback, 'function', {
-      moduleName: 'workbox-core',
-      funcName: 'register',
-      paramName: 'callback',
-    });
-  }
-
-  callbacks.add(callback);
-
-  if (process.env.NODE_ENV !== 'production') {
-    logger.log('Registered a callback to respond to quota errors.', callback);
-  }
-}
-
-/**
- * Runs all of the callback functions, one at a time sequentially, in the order
- * in which they were registered.
- *
- * @memberof workbox.core
- * @private
- */
-async function executeQuotaErrorCallbacks() {
-  if (process.env.NODE_ENV !== 'production') {
-    logger.log(`About to run ${callbacks.size} callbacks to clean up caches.`);
-  }
-
-  for (const callback of callbacks) {
-    await callback();
-    if (process.env.NODE_ENV !== 'production') {
-      logger.log(callback, 'is complete.');
-    }
-  }
-
-  if (process.env.NODE_ENV !== 'production') {
-    logger.log('Finished running callbacks.');
-  }
-}
-
-export {
-  executeQuotaErrorCallbacks,
-  registerQuotaErrorCallback,
-};
diff --git a/packages/workbox-core/models/quotaErrorCallbacks.mjs b/packages/workbox-core/models/quotaErrorCallbacks.mjs
new file mode 100644
index 000000000..72e362844
--- /dev/null
+++ b/packages/workbox-core/models/quotaErrorCallbacks.mjs
@@ -0,0 +1,15 @@
+/*
+  Copyright 2018 Google LLC
+
+  Use of this source code is governed by an MIT-style
+  license that can be found in the LICENSE file or at
+  https://opensource.org/licenses/MIT.
+*/
+
+import '../_version.mjs';
+
+
+// Callbacks to be executed whenever there's a quota error.
+const quotaErrorCallbacks = new Set();
+
+export {quotaErrorCallbacks};
diff --git a/packages/workbox-core/registerQuotaErrorCallback.mjs b/packages/workbox-core/registerQuotaErrorCallback.mjs
index 2e10f3a1e..93d4c87e8 100644
--- a/packages/workbox-core/registerQuotaErrorCallback.mjs
+++ b/packages/workbox-core/registerQuotaErrorCallback.mjs
@@ -6,8 +6,33 @@
   https://opensource.org/licenses/MIT.
 */
 
-import {registerQuotaErrorCallback} from './_private/quota.mjs';
+import {logger} from './_private/logger.mjs';
+import {assert} from './_private/assert.mjs';
+import {quotaErrorCallbacks} from './models/quotaErrorCallbacks.mjs';
 import './_version.mjs';
 
 
+/**
+ * Adds a function to the set of quotaErrorCallbacks that will be executed if
+ * there's a quota error.
+ *
+ * @param {Function} callback
+ * @memberof workbox.core
+ */
+function registerQuotaErrorCallback(callback) {
+  if (process.env.NODE_ENV !== 'production') {
+    assert.isType(callback, 'function', {
+      moduleName: 'workbox-core',
+      funcName: 'register',
+      paramName: 'callback',
+    });
+  }
+
+  quotaErrorCallbacks.add(callback);
+
+  if (process.env.NODE_ENV !== 'production') {
+    logger.log('Registered a callback to respond to quota errors.', callback);
+  }
+}
+
 export {registerQuotaErrorCallback};
diff --git a/test/all/node/test-exports.mjs b/test/all/node/test-exports.mjs
index e4e4e1ac6..4945249f9 100644
--- a/test/all/node/test-exports.mjs
+++ b/test/all/node/test-exports.mjs
@@ -73,4 +73,50 @@ describe(`[all] Window and SW packages`, function() {
           .to.deep.equal(topLevelFiles.concat(deprecatedExports).sort());
     }
   });
+
+  it(`should have top a level module for every export in _private.mjs (and vise-versa)`, async function() {
+    for (const pkg of windowAndBrowserPackages) {
+      const packagePath = path.join(__dirname, '..', '..', '..', 'packages', pkg.name);
+      const privateFile = path.join(packagePath, '_private.mjs');
+
+      // Only some packages have a `_private.mjs` module.
+      if (!fs.existsSync(privateFile)) {
+        continue;
+      }
+
+      const privateContents = await fs.readFile(privateFile, 'utf-8');
+
+      // Use the acorn parser to generate a list of named exports.
+      const namedExports = [];
+      const indexAST = acorn.parse(privateContents, {
+        ecmaVersion: 6,
+        sourceType: 'module',
+      });
+      for (const node of indexAST.body) {
+        if (node.type === 'ExportDefaultDeclaration') {
+          throw new Error(`'_private.mjs' files cannot contain default exports`);
+        }
+        if (node.type === 'ExportNamedDeclaration') {
+          if (node.specifiers.length === 0) {
+            throw new Error(`'_private.mjs' files may only contain a single, named-export block`);
+          }
+          for (const specifier of node.specifiers) {
+            namedExports.push(specifier.exported.name);
+          }
+        }
+      }
+
+      // Inspect the package directory to get a list of top-level, public
+      // module basenames.
+      const privateDirectoryPath = path.join(packagePath, '_private');
+      const topLevelFiles = glob.sync('*.mjs', {cwd: privateDirectoryPath})
+          .map((file) => path.basename(file, '.mjs'));
+
+      const deprecatedExports = deprecatedPackageExports[pkg.name] || [];
+
+      // Assert there's a 1-to-1 mapping between exports and top-level files.
+      expect(namedExports.sort())
+          .to.deep.equal(topLevelFiles.concat(deprecatedExports).sort());
+    }
+  });
 });
diff --git a/test/workbox-core/sw/_private/test-cacheWrapper.mjs b/test/workbox-core/sw/_private/test-cacheWrapper.mjs
index d3f2eb395..44904e1c7 100644
--- a/test/workbox-core/sw/_private/test-cacheWrapper.mjs
+++ b/test/workbox-core/sw/_private/test-cacheWrapper.mjs
@@ -7,7 +7,7 @@
 */
 
 import {cacheWrapper} from 'workbox-core/_private/cacheWrapper.mjs';
-import {registerQuotaErrorCallback} from 'workbox-core/_private/quota.mjs';
+import {registerQuotaErrorCallback} from 'workbox-core/registerQuotaErrorCallback.mjs';
 
 
 describe(`cacheWrapper`, function() {
diff --git a/test/workbox-core/sw/_private/test-checkSWFileCacheHeaders.mjs b/test/workbox-core/sw/_private/test-checkSWFileCacheHeaders.mjs
deleted file mode 100644
index b3fde1d79..000000000
--- a/test/workbox-core/sw/_private/test-checkSWFileCacheHeaders.mjs
+++ /dev/null
@@ -1,131 +0,0 @@
-/*
-  Copyright 2018 Google LLC
-
-  Use of this source code is governed by an MIT-style
-  license that can be found in the LICENSE file or at
-  https://opensource.org/licenses/MIT.
-*/
-
-import {logger} from 'workbox-core/_private/logger.mjs';
-import {checkSWFileCacheHeaders} from 'workbox-core/_private/checkSWFileCacheHeaders.mjs';
-
-
-describe(`checkSWFileCacheHeaders`, function() {
-  let sandbox = sinon.createSandbox();
-
-  beforeEach(function() {
-    if (process.env.NODE_ENV !== 'production') {
-      sandbox.stub(logger);
-    }
-  });
-
-  afterEach(function() {
-    sandbox.restore();
-  });
-
-  it(`should handle bad response`, async function() {
-    if (process.env.NODE_ENV === 'production') this.skip();
-
-    sandbox.stub(self, 'fetch').callsFake(async () => {
-      return new Response('Not Found.', {
-        status: 404,
-      });
-    });
-
-    await checkSWFileCacheHeaders();
-
-    expect(logger.warn.callCount).to.equal(0);
-  });
-
-  it(`should handle no cache-control header`, async function() {
-    if (process.env.NODE_ENV === 'production') this.skip();
-
-    sandbox.stub(self, 'fetch').callsFake(async () => {
-      return new Response('OK');
-    });
-
-    await checkSWFileCacheHeaders();
-
-    expect(logger.warn.callCount).to.equal(0);
-  });
-
-  it(`should log for bad cache-control header`, async function() {
-    if (process.env.NODE_ENV === 'production') this.skip();
-
-    sandbox.stub(self, 'fetch').callsFake(async () => {
-      return new Response('OK', {
-        headers: {
-          'cache-control': 'max-age=2000',
-        },
-      });
-    });
-
-    await checkSWFileCacheHeaders();
-
-    expect(logger.warn.callCount).to.equal(1);
-  });
-
-  it(`should handle unexpected max-age cache-control header`, async function() {
-    if (process.env.NODE_ENV === 'production') this.skip();
-
-    sandbox.stub(self, 'fetch').callsFake(async () => {
-      return new Response('OK', {
-        headers: {
-          'cache-control': 'max-age=abc',
-        },
-      });
-    });
-
-    await checkSWFileCacheHeaders();
-
-    expect(logger.warn.callCount).to.equal(1);
-  });
-
-  it(`should NOT log for max-age=0 cache-control header`, async function() {
-    if (process.env.NODE_ENV === 'production') this.skip();
-
-    sandbox.stub(self, 'fetch').callsFake(async () => {
-      return new Response('OK', {
-        headers: {
-          'cache-control': 'max-age=0',
-        },
-      });
-    });
-
-    await checkSWFileCacheHeaders();
-
-    expect(logger.warn.callCount).to.equal(0);
-  });
-
-  it(`should NOT log for no-cache cache-control header`, async function() {
-    if (process.env.NODE_ENV === 'production') this.skip();
-
-    sandbox.stub(self, 'fetch').callsFake(async () => {
-      return new Response('OK', {
-        headers: {
-          'cache-control': 'no-cache',
-        },
-      });
-    });
-
-    await checkSWFileCacheHeaders();
-
-    expect(logger.warn.callCount).to.equal(0);
-  });
-
-  it(`should NOT log for no-store cache-control header`, async function() {
-    if (process.env.NODE_ENV === 'production') this.skip();
-
-    sandbox.stub(self, 'fetch').callsFake(async () => {
-      return new Response('OK', {
-        headers: {
-          'cache-control': 'no-cache',
-        },
-      });
-    });
-
-    await checkSWFileCacheHeaders();
-
-    expect(logger.warn.callCount).to.equal(0);
-  });
-});
diff --git a/test/workbox-core/sw/_private/test-executeQuotaErrorCallbacks.mjs b/test/workbox-core/sw/_private/test-executeQuotaErrorCallbacks.mjs
new file mode 100644
index 000000000..faa44a3ec
--- /dev/null
+++ b/test/workbox-core/sw/_private/test-executeQuotaErrorCallbacks.mjs
@@ -0,0 +1,55 @@
+/*
+  Copyright 2018 Google LLC
+
+  Use of this source code is governed by an MIT-style
+  license that can be found in the LICENSE file or at
+  https://opensource.org/licenses/MIT.
+*/
+
+import {executeQuotaErrorCallbacks} from 'workbox-core/_private/executeQuotaErrorCallbacks.mjs';
+import {registerQuotaErrorCallback} from 'workbox-core/registerQuotaErrorCallback.mjs';
+
+
+describe(`executeQuotaErrorCallbacks()`, function() {
+  const sandbox = sinon.createSandbox();
+
+  afterEach(function() {
+    sandbox.restore();
+  });
+
+  it('should call everything registered with registerQuotaErrorCallback()', async function() {
+    const callback1 = sandbox.stub();
+    registerQuotaErrorCallback(callback1);
+    const callback2 = sandbox.stub();
+    registerQuotaErrorCallback(callback2);
+
+    await executeQuotaErrorCallbacks();
+
+    expect(callback1.calledOnce).to.be.true;
+    expect(callback2.calledOnce).to.be.true;
+  });
+
+  it(`shouldn't have any effect if called multiple times with the same callback`, async function() {
+    const callback1 = sandbox.stub();
+    registerQuotaErrorCallback(callback1);
+    registerQuotaErrorCallback(callback1);
+    registerQuotaErrorCallback(callback1);
+
+    await executeQuotaErrorCallbacks();
+
+    expect(callback1.calledOnce).to.be.true;
+  });
+
+  it(`should call everything registered with registerQuotaErrorCallback(), each time it's called`, async function() {
+    const callback1 = sandbox.stub();
+    registerQuotaErrorCallback(callback1);
+    const callback2 = sandbox.stub();
+    registerQuotaErrorCallback(callback2);
+
+    await executeQuotaErrorCallbacks();
+    await executeQuotaErrorCallbacks();
+
+    expect(callback1.calledTwice).to.be.true;
+    expect(callback2.calledTwice).to.be.true;
+  });
+});
diff --git a/test/workbox-core/sw/_private/test-quota.mjs b/test/workbox-core/sw/_private/test-quota.mjs
deleted file mode 100644
index 067cdf8a3..000000000
--- a/test/workbox-core/sw/_private/test-quota.mjs
+++ /dev/null
@@ -1,64 +0,0 @@
-/*
-  Copyright 2018 Google LLC
-
-  Use of this source code is governed by an MIT-style
-  license that can be found in the LICENSE file or at
-  https://opensource.org/licenses/MIT.
-*/
-
-import {executeQuotaErrorCallbacks, registerQuotaErrorCallback} from 'workbox-core/_private/quota.mjs';
-
-
-describe(`quota`, function() {
-  describe(`registerQuotaErrorCallback()`, function() {
-    it(`should throw when passed a non-function in dev mode`, async function() {
-      if (process.env.NODE_ENV === 'production') this.skip();
-
-      await expectError(() => registerQuotaErrorCallback(null), 'incorrect-type');
-    });
-  });
-
-  describe(`executeQuotaErrorCallbacks()`, function() {
-    const sandbox = sinon.createSandbox();
-
-    afterEach(function() {
-      sandbox.restore();
-    });
-
-    it('should call everything registered with registerQuotaErrorCallback()', async function() {
-      const callback1 = sandbox.stub();
-      registerQuotaErrorCallback(callback1);
-      const callback2 = sandbox.stub();
-      registerQuotaErrorCallback(callback2);
-
-      await executeQuotaErrorCallbacks();
-
-      expect(callback1.calledOnce).to.be.true;
-      expect(callback2.calledOnce).to.be.true;
-    });
-
-    it(`shouldn't have any effect if called multiple times with the same callback`, async function() {
-      const callback1 = sandbox.stub();
-      registerQuotaErrorCallback(callback1);
-      registerQuotaErrorCallback(callback1);
-      registerQuotaErrorCallback(callback1);
-
-      await executeQuotaErrorCallbacks();
-
-      expect(callback1.calledOnce).to.be.true;
-    });
-
-    it(`should call everything registered with registerQuotaErrorCallback(), each time it's called`, async function() {
-      const callback1 = sandbox.stub();
-      registerQuotaErrorCallback(callback1);
-      const callback2 = sandbox.stub();
-      registerQuotaErrorCallback(callback2);
-
-      await executeQuotaErrorCallbacks();
-      await executeQuotaErrorCallbacks();
-
-      expect(callback1.calledTwice).to.be.true;
-      expect(callback2.calledTwice).to.be.true;
-    });
-  });
-});
diff --git a/test/workbox-core/sw/test-registerQuotaErrorCallback.mjs b/test/workbox-core/sw/test-registerQuotaErrorCallback.mjs
new file mode 100644
index 000000000..e9d22c977
--- /dev/null
+++ b/test/workbox-core/sw/test-registerQuotaErrorCallback.mjs
@@ -0,0 +1,18 @@
+/*
+  Copyright 2018 Google LLC
+
+  Use of this source code is governed by an MIT-style
+  license that can be found in the LICENSE file or at
+  https://opensource.org/licenses/MIT.
+*/
+
+import {registerQuotaErrorCallback} from 'workbox-core/registerQuotaErrorCallback.mjs';
+
+
+describe(`registerQuotaErrorCallback()`, function() {
+  it(`should throw when passed a non-function in dev mode`, async function() {
+    if (process.env.NODE_ENV === 'production') this.skip();
+
+    await expectError(() => registerQuotaErrorCallback(null), 'incorrect-type');
+  });
+});
diff --git a/test/workbox-expiration/sw/test-Plugin.mjs b/test/workbox-expiration/sw/test-Plugin.mjs
index 0a06e383e..d389fa775 100644
--- a/test/workbox-expiration/sw/test-Plugin.mjs
+++ b/test/workbox-expiration/sw/test-Plugin.mjs
@@ -9,7 +9,7 @@
 import {Plugin} from 'workbox-expiration/Plugin.mjs';
 import {CacheExpiration} from 'workbox-expiration/CacheExpiration.mjs';
 import {cacheNames} from 'workbox-core/_private/cacheNames.mjs';
-import {executeQuotaErrorCallbacks} from 'workbox-core/_private/quota.mjs';
+import {executeQuotaErrorCallbacks} from 'workbox-core/_private/executeQuotaErrorCallbacks.mjs';
 
 
 describe(`Plugin`, function() {