Popular third-party mail client Sparrow was recently bought by Google, but that hasn’t stopped the app’s developers from pushing out updates for their existing user base. Today Sparrow for iPhone received a long-awaited update that brings support for the iPhone 5’s taller display and iOS 6’s Passbook.

This very update was rejected by Apple earlier this month because of a mixup with Rich Text support in iOS 5. Sparrow has obviously ironed out the kinks with Apple, as users can download the update now in the App Store.

Just a day after releasing Sparrow 1.2 for iPhone, the Sparrow team has issued an update to Sparrow for Mac. This release brings a number of new features, improves Sparrow startup times, and quashes bugs.

Sparrow for iPhone — the third-party email client that has left Apple’s built-in Mail app redundant on my device — has received another major update today, which introduces a number of helpful features and quashes a handful of bugs.

One thing it doesn’t add, however, is that much-anticipated push support. That’s coming later, but you’ll have to pay for it.

Sparrow for iPhone just got its first update since hitting the App Store last month, and it already brings several new features, including a built-in web browser, customizable icon badges, and clever archiving. There’s still no push function, however, Sparrow promises its coming, “with or without Apple.”

A new jailbreak tweak adds push notifications to the popular iPhone email app called Sparrow. We’ve already shown you a roundabout way to get push for Sparrow with the Boxcar app on a non-jailbroken iPhone, but you can now easily enable notifications with a Cydia tweak called Sparrow Push.