I can think of two ways that you can change compression:
1) Thicker Head Gaskets
2) Changing Pistons.....The size, shape, and combustion areas on the piston determine if the compression ration rasies / lowers
As far as HP and compression
Take a Camry...
The 5SFE makes 130hp with a 9.5:1 CR. Now if you were to raise that to 10:1 you would make some more horsepower. If you lower the CR to 8.5:1 you will go down in horsepower [all of this is also dependent on tuning]
HOWEVER, lower CR allows for you to to introduce more forced induction, i.e a turbo. So although your naturally aspirated HP rating went down, you can now add a Turbo and have much more the 130hp......
Hope that helped