-From Punisher's log; get the barbell "deep" in your hands. Don't hold it in your fingers, grab the bar deep in the crease of your thumb, just like bench pressing. This keeps the bar over the bones of your forearm, instead of supported by your hands with your wrists all folded back. Straight wrists make your elbows and upper back and everything line up reeal nice.
-Lower body and midsection locked in, almost like the top of squat. This doesn't always come natural for me. For warm-ups, I loop a band over my belt, then step through the ends of the band. It tries to bend you over forward, any you really have to drive with the abs, hips and glutes, brace and spread the floor, to stay upright. After a few light sets, remove the band and you'll feel like a pillar.
I like to hit some bottoms up kettlebell presses before real presses. You have to get good wrist position and upper back tightness to press the bell. Its like a more strict press. If you do them in the half kneeling position they can get your hips and mid section warmed up to press too.
Pull aparts are good. Don't forget to do some with bent arms, almost trying to recreate the bottom of a press. And some with an under handed grip. Or some bent forward at the waist. Learn to get tight at a bunch of different angles.
I'm also taking Yogi's advice and working on my lower traps. Prone trap raises, and snatch grip shrugs, leaning forward in the Smith machine. And I just started doing Yates rows to copy Bauber. So hopefully those will help my press.
Its really easy to add some seated dumbbell presses, or high incline dumbbell presses as assistance on bench press day. Dumbbells always help me with bar-path. And maybe shoulder size, but that could be all in my head.