The primary function of the rotator cuff (which many people often miss) is to center the humeral head in the glenoid fossa. In order to accomplish this, the dynamic stabilizers of the shoulder need to be on their "A" game. This is of special consideration when dealing with athletes, as the nature of competition is frequently an "open loop" scenario. See the video below for a pushup variation that incorporates some dynamic stabilization of the shoulder girdle. We named it "Suspended Pushup ISO Hold (with perturbations) into Repetitions."

A couple notes:

Having a studly powerlifter give you perturbations during the ISO hold is optional, as the suspension straps inherently provide a stability challenge on their own.
This exercise hits multiple birds with one stone. It will give you a tremendous challenge for your core (you're essentially holding a plank position for the entire time), give you a nice stretch for the pecs in the bottom, improve the ability of your rotator cuff to stabilize the humeral head (where your upper arm bone attaches to the shoulder joint), and develop your upper body strength. Sounds like a winner to me.
As shown in the video, hold at the bottom for 10-20 seconds, and then move into the desired number of repetitions. Stay TIGHT in the bottom. Everything should be braced. Everything....
Using the suspension straps is actually a fairly advanced progression of a pushup (especially if your feet are elevated, as shown). Be sure you master the ground-based pushups first.
(Piggybacking off of #2) If you don't have access to suspension straps (or a partner), no problem! Holding a tight isometric at the bottom of a pushup (on the floor), and then moving into repetitions, can make a great way of taking on a new challenge if standard pushups have become a bit easy for you.
You increase testosterone levels by 50% if you wear a "Do Work" shirt while performing these.

Just don't tear your shoulder in two....Stevo