There are several pressing exercises that I utilize during my shoulder workouts (Behind-the-Neck Presses, Front Barbell Presses, Dumbbell Presses, and Arnold Presses) and not all in the same workout, mind you.
With the dumbbells I lower the weight well below my upper arms being parallel to the floor. I like the stretch and range of motion and it doesn't bother my shoulders.
With the barbells, other than push presses, going below parallel seems to bring my triceps in more than my delts. The past few times I did barbell work, I felt like I'd done a triceps routine versus a shoulder one.
I'm not a huge fan of short ranges of motion, but that might be the only way to go for a while. Usually, my hands grab the bar about an inch out from my shoulders. I raise the bar to almost locking out then lower to touching my traps for a second, then lift again. How low does the bar need to go?

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I'm trying everything to minimize triceps involvement and I'm really struggling. Any advice on hand position or range of motion would really be appreciated.
Thanks guys...and gals (sorry Iron Kitten).