diff --git a/index.ts b/index.ts
index f156820..b1d28bc 100644
--- a/index.ts
+++ b/index.ts
@@ -68,18 +68,21 @@ async function get<TValue extends Value>(key: string): Promise<TValue | undefine
 }
 
 async function set<TValue extends Value>(key: string, value: TValue, maxAge: TimeDescriptor = {days: 30}): Promise<TValue> {
-	if (typeof value === 'undefined') {
-		// @ts-expect-error This never happens in TS because `value` can't be undefined
-		return;
+	if (arguments.length < 2) {
+		throw new TypeError('Expected a value as the second argument');
 	}
 
-	const internalKey = `cache:${key}`;
-	await storageSet({
-		[internalKey]: {
-			data: value,
-			maxAge: timeInTheFuture(maxAge)
-		}
-	});
+	if (typeof value === 'undefined') {
+		await delete_(key);
+	} else {
+		const internalKey = `cache:${key}`;
+		await storageSet({
+			[internalKey]: {
+				data: value,
+				maxAge: timeInTheFuture(maxAge)
+			}
+		});
+	}
 
 	return value;
 }
diff --git a/test/index.js b/test/index.js
index 74c5040..873cf23 100644
--- a/test/index.js
+++ b/test/index.js
@@ -64,10 +64,15 @@ test.serial('has() with expired cache', async t => {
 	t.is(await cache.has('name'), false);
 });
 
+test.serial('set() without a value', async t => {
+	await t.throwsAsync(cache.set('name'), {instanceOf: TypeError, message: 'Expected a value as the second argument'});
+});
+
 test.serial('set() with undefined', async t => {
-	await cache.set('name');
-	// StorageArea.set should not be called with `undefined`
-	t.is(chrome.storage.local.set.callCount, 0);
+	await cache.set('name', 'Anne');
+	await cache.set('name', undefined);
+	// Cached value should be erased
+	t.is(await cache.has('name'), false);
 });
 
 test.serial('set() with value', async t => {