To raise an engine's compression you have to increase the cylinder volume as opposed to the combustion volume. To increase cylinder volume you will have to bore out the engine or you could stroke the engine which is increasing the length the piston travels inside the cylinder.
To do either of these you should plan ahead and you'll need new internals. New crankshaft allows the piston to travel further. I believe the piston rods stay the same length though and you can change the the height (thickness) of a piston (I believe sometimes) unless you bore out the engine in which case you will need to get new pistons, larger diameter ones to be specific.
Just as an example, a lot of 302cid (5.0L) like to bore out the engine to a 306cid.