A height of less than 5 inches limits you to the Motorola Droid Mini, Moto E or the recently released LG Joy. (Those 3 run Lollipop and are from 2013 and later.)

Increasing height to 5.1 inches (well, 130mm), gsmarena.com shows almost a dozen phones that suit your wishes.

(Personally, I'm still not happy about having to give up on having a hardware QWERTY keyboards on my phone :/ )