Delta - No Min.
In fact, there are some people who "drop" their whole line and get a whole new schedule from available trips. It's a little harder in the summer because we're short right now so dropping trips in general doesn't always have enough reserve coverage. We also can bid that way where you can put in to only be awarded what you've asked for and if you don't get anything you don't have to pick up anything. I believe this is why if a pilot is senior (your 60-65 age group) they can be very selective about their lines if only to maintain insurance coverage. While DAL's medical is fairly mediocre it is Gold Plated compared to what's available from the state's with an Obamacare exchange (just looked and for a 58 y.o. male it is $500/month with a $6,000 deductible so $12,000 out of pocket before insurance pays a dime.