Freshly public T-Mobile (NASDAQ:TMUS) has just released first-quarter earnings, and things are starting to look up for the No. 4 domestic carrier that just merged with No. 5 carrier MetroPCS. The company just posted its first positive growth in branded customer net additions since 2009.

However, it's still too early to proclaim that this improvement is due to its bold new "un-carrier" initiative or the introduction of Apple's (NASDAQ:AAPL) iPhone. That's because those two changes were announced at the very end of March with just days left in the quarter. The iPhone wouldn't launch on T-Mobile until early April, after the quarter closed.

Speaking of the iPhone, T-Mobile has sold roughly 500,000 so far in a little less than a month. Not a bad start considering that translates into a quarterly run rate of about 1.5 million, which is how many iPhones than larger rival Sprint Nextel (NYSE:S) sold during the first quarter.

That jump right out the gate can be attributed to pent-up demand within T-Mobile's subscriber base, as well as the fact that T-Mobile offers the iPhone 5 for just $99 up front while the larger carriers normally charge $200. Sprint is currently running a $100 switching promotion for new customers, which brings its entry-level iPhone price down to $100.

T-Mobile is making progress with cutting its branded customer losses. The 3,000 net additions may not seem like a lot, but it's much better than bleeding more. The carrier has dramatically improved postpaid churn while also growing prepaid subscribers.

Total branded customers now stand at 26.1 million, which consists of 20.1 million postpaid and 6 million prepaid subscribers. The wholesale business is also growing, with T-Mobile growing its MVNO customer base by 21% to 4.6 million. The wholesale side is where T-Mobile is seeing the most growth in overall customer additions.

The un-carrier is starting to turn the boat around with its most important operating metrics, but its new messaging is still a little misleading at times, since most customers are still locked in to two years of service. The only difference is that it's an installment plan instead of a service contract that's tying them down.