Another option is the Nokia 3 or Nokia 3.1. Yes, Nokia makes Android phones, they're really good, and one is pretty small.
The Nokia 3 packs a 5-inch 720p display, runs nearly stock Android, and costs less than $200. So if you want a small(er) phone without breaking the bank, this is worth considering.
For under $150 you'll get a decent 5-inch screen, quad-core MediaTek processor with 2GB of RAM, 16GB of storage and a microSD slot for expansion up to 256GB. Then, there's an 8MP front and 8MP rear camera setup, Android 8 Oreo, and a 2,630 mAh battery.
Buy it Now on Amazon for $175, or an unlocked model that works great in the US for $220.
Personally, we recommend the newer Nokia 3.1 (2018) with a 5.2-inch screen for just $149. Or even the Nokia 7.1 with a 5.8-inch screen, as it's still pretty small.