The galaxy s4 mini has been leaked: http://www.sammobile.com/2013/03/22/...alaxy-s4-mini/
4.3" qHD (960x540). Screen tech is rumored to be labeled "Super AMOLED", which so far has only been applied to pentile screens, but "HD Super AMOLED" included the non-pentile Note 2. At 256ppi, it would be a respectable non-pentile density (Note 2 is 260ish), but if it's pentile, it would need to be a lot higher before I'd consider it as a replacement for my primary reader.
Offhand, it sort of appears they weren't as aggressive with the s4 mini bezel as they were with the s4 bezel.
Internal specs, on the other hand, sound impressive. Sammobile
, purveyor of many true and untrue leaks, thinks it may have a Exynos 5 dual or quad (with the quad maybe alternating arm7/15 like the octa, not necessarily 4 simultaneous cores). If true, that's a much smaller downgrade from the s4 than the s3 mini was from the s3.