By the way, this is exactly how submarines used to change depth (Modern subs tend to use a different method). They have sections that can be filled with water or air, and tanks of compressed air. If they need to come up quickly, they let some of the compressed air into those sections, pushing out the water. This is like your syringe example.

A modern sub is more likely to use that process to get almost exactly zero buoyancy, and then change depth by pointing a bit up or down while running the propeller.