This exercise builds brutal strength and core stability. When you use dumbbells instead of a barbell, your core works to stabilize the unbalanced load. This provides a wicked anti-lateral flexion component, hitting your obliques harder than a medicine ball to the gut.
Single-arm dumbbell presses, done with heavy weight, can be used as a pure strength movement to build bigger shoulders and to give you a resilient mid-section.
Keep your feet shoulder width or slightly wider and brace your abs. Extend the non-working arm to your side, hold it on your hip, or drape it across your body onto your obliques.
Just as you do with a bilateral overhead press, create a shelf by keeping your elbows up to engage your lats. This puts the arm in a safer position to press overhead. Then lock out at the top of each rep. Finish in a joint-stacked position.