Need help recommending an Android phone smaller than 5 inches.

Hi all! I'm worried that what I'm looking for doesn't exist, but here it goes. My girlfriend wants to replace her HTC Incredible II from two years ago. Here is the criteria:

- High end (Incredible II was high end when it was new)

- Smaller than 5 inch screen. This is important to her.

- Good battery life.

- Carrier: Verizon, USA

Does such a phone exist? Thanks in advance!