And when the person who holds the world record in a certain lift has an accessory movement named after him, I pay attention.
That said, I began performing the Savickas press (also called the Z press) out of necessity---the ceiling in my basement is too low for me to do standing overhead presses, so I needed an alternative. It was fortuitous, because my abs are my weak link on my overhead press, and the Savickas press is murder on the abs.
The lift is simple: it's an overhead press, but instead of standing, or sitting on a bench, you sit on the floor, legs splayed in front of you. It is very difficult to remain upright in this position, especially when pressing a weight overhead.
Caveat: if you don't have sterling thoracic and shoulder mobility, this exercise is a bad idea -- and actually, overhead pressing in general might be temporarily beyond the scope of your ability. (Read this post from strength coach and Professional Awesome Person Tony Gentilcore to learn more about which side of the line you fall.)
You could do these bilaterally with a barbell if you have a power rack, but I like the single-arm version with a dumbbell or kettlebell. It's easier to get into position, and adds a component of lateral stability into the lift. If you're new to these, go LIGHT and prepare to feel uncharted ab soreness the day after. I like these for higher rep sets of 8-10, but also occasionally go for heavier triples. Check it out: