From experience that doesn't work unless your acetomiophen has caffein in it. Ibuprofen, naproxen, nothing helps, but caffein.
To get off a caffein addiction and avoid headaches, you need about 5 days where you taper your intake.
Day 1: 1 cup of coffee Day 2: 1/2 cup Day3: 1/4 cup Day 4: 1/8 cup Day 5: two small sips Day 6: Freedom!
I've repeated this experiment three times. Works like a charm.