Unihertz makes a few niche phones, check out their sizes. They are updating the Jelly line (3" screen, might be too small for you, but is what I own) right now

Unihertz makes a few niche phones, check out their sizes. They are updating the Jelly line (3" screen, might be too small for you, but is what I own) right now for a fall release. The Atom XL is a ruggedized phone with a slightly larger (4") screen. FWIW, those both are thicker than an iphone mini (gotta fit the battery somewhere I guess). [edit] There is also the Titan Slim. It's a 4.2 inch screen, but has a keyboard, making it narrow, but very tall (5.75"). And if you do go for the super tiny Jelly series, don't get the 2E; it's designed as a second phone and so is less well spec'd than the older Jelly 2 (or the upcoming Jelly Star).