ACE says many common gym exercises intended to target the tummy (like bicycle crunches and stability ball crunches), while engaging two of the the main muscles that make up what you think of as your "core" (your rectus abdominis and your obliques), place too much pressure on your spine. Doing the following exercises is a better approach to a flat tummy and a stable, strong lower back:
1. Front Plank - These build strength and endurance, says ACE. A front plank involves laying on your stomach with your elbows close to your sides and directly under your shoulders, palms down and fingers facing forward, then engaging your abdominal and thigh muscles to straighten your legs, flex your ankles and slowly lift your torso and thighs off the floor. ACE has detailed instructions here.
2. Side Plank - A variation on the above (instead of starting on your stomach, you start and lift up on one side), this move works core muscles and helps build stability in your spine.
3. Bird Dog - To do a "bird dog," start on your hands and knees, engage your core muscles and lift your opposite arm and leg simultaneously. Providing an excellent challenge to your abdominal muscles, ACE says this move (instructions here) also trains your lower back to be stable during movement.