My 2 cents -- I found one day that one shoulder was really going to crap. Eventually I completely stopped lifting at all for many months. When I came back, once I gradually eased back on up in weights & paid more attention to shoulder flexibility, I began doing this for Deadlifts, essentially:
Warmup -- Hang power Olympic pulls (Hang power snatch/hang power clean/high pull)
once that weight is too much, then
continue Warmup -- Overhand deadlift
Once that weight is too much, then
Workset Deadlift -- Alternate each set hand position:
Odd sets (set 1, 3, 5 etc (rarely do that many though)) -- Left under, Right over
Even Sets (set 2, 4, 6, etc (ditto)) -- Right under, Left over