Adding on to what mjf314 said, there is actually a tag on MDL for Japanese Asadora if you want to see which are more popular with users or rated higher. Webdramas also tend to have shorter episodes!
For really short 15-min episode dramas I've loved this one:
The Sound of Your Heart*- hilarious and short 15 min episodes (Netflix shoves 2 episodes into 1 to make it 30 min, but you can still clearly see when an episodes starts and another ends. Episodes are also episodic so it's "easier" to not give in and binge)
Others I've watched and liked which have slightly longer episodes, around 20-25 minutes: Addicted, History: Boundary Crossing, History: Right or Wrong, History: Stay Away From Me, Transit Girls; and one with 30 min: Ito-Kun A to E*
(* are those I recommend most)
From what I've seen those with shorter episodes also have short runs, so if you want something that'll last you a while your best bet is a japanese morning drama (asadora). I never finished one yet, although I started watching Carnation before I had MDL and ended up forgetting which ep I was on OTL I did enjoy what I watched though and do plan on starting over one of these days ^^
