diff --git a/utils.test.ts b/utils.test.ts
index ac39e9f..4f11546 100644
--- a/utils.test.ts
+++ b/utils.test.ts
@@ -1,6 +1,12 @@
 import { describe, test, expect } from 'bun:test'
 import { buildEvent } from './test-helpers.ts'
-import { Queue, insertEventIntoAscendingList, insertEventIntoDescendingList, binarySearch } from './utils.ts'
+import {
+  Queue,
+  insertEventIntoAscendingList,
+  insertEventIntoDescendingList,
+  binarySearch,
+  normalizeURL,
+} from './utils.ts'
 
 import type { Event } from './core.ts'
 
@@ -263,3 +269,43 @@ test('binary search', () => {
   expect(binarySearch(['a', 'b', 'd', 'e'], b => ('a' < b ? -1 : 'a' === b ? 0 : 1))).toEqual([0, true])
   expect(binarySearch(['a', 'b', 'd', 'e'], b => ('[' < b ? -1 : '[' === b ? 0 : 1))).toEqual([0, false])
 })
+
+describe('normalizeURL', () => {
+  test('normalizes wss:// URLs', () => {
+    expect(normalizeURL('wss://example.com')).toBe('wss://example.com/')
+    expect(normalizeURL('wss://example.com/')).toBe('wss://example.com/')
+    expect(normalizeURL('wss://example.com//path')).toBe('wss://example.com/path')
+    expect(normalizeURL('wss://example.com:443')).toBe('wss://example.com/')
+  })
+
+  test('normalizes https:// URLs', () => {
+    expect(normalizeURL('https://example.com')).toBe('wss://example.com/')
+    expect(normalizeURL('https://example.com/')).toBe('wss://example.com/')
+    expect(normalizeURL('http://example.com//path')).toBe('ws://example.com/path')
+  })
+
+  test('normalizes ws:// URLs', () => {
+    expect(normalizeURL('ws://example.com')).toBe('ws://example.com/')
+    expect(normalizeURL('ws://example.com/')).toBe('ws://example.com/')
+    expect(normalizeURL('ws://example.com//path')).toBe('ws://example.com/path')
+    expect(normalizeURL('ws://example.com:80')).toBe('ws://example.com/')
+  })
+
+  test('adds wss:// to URLs without scheme', () => {
+    expect(normalizeURL('example.com')).toBe('wss://example.com/')
+    expect(normalizeURL('example.com/')).toBe('wss://example.com/')
+    expect(normalizeURL('example.com//path')).toBe('wss://example.com/path')
+  })
+
+  test('handles query parameters', () => {
+    expect(normalizeURL('wss://example.com?z=1&a=2')).toBe('wss://example.com/?a=2&z=1')
+  })
+
+  test('removes hash', () => {
+    expect(normalizeURL('wss://example.com#hash')).toBe('wss://example.com/')
+  })
+
+  test('throws on invalid URL', () => {
+    expect(() => normalizeURL('http://')).toThrow('Invalid URL: http://')
+  })
+})
diff --git a/utils.ts b/utils.ts
index a2e68b3..c08d697 100644
--- a/utils.ts
+++ b/utils.ts
@@ -9,6 +9,8 @@ export function normalizeURL(url: string): string {
   try {
     if (url.indexOf('://') === -1) url = 'wss://' + url
     let p = new URL(url)
+    if (p.protocol === 'http:') p.protocol = 'ws:'
+    else if (p.protocol === 'https:') p.protocol = 'wss:'
     p.pathname = p.pathname.replace(/\/+/g, '/')
     if (p.pathname.endsWith('/')) p.pathname = p.pathname.slice(0, -1)
     if ((p.port === '80' && p.protocol === 'ws:') || (p.port === '443' && p.protocol === 'wss:')) p.port = ''