Despite the fact that it contains no valves, and could basically be replaced with a flat slab of aluminum, the cylinder head in a two stroke engine has had an incredible amount of research done on it. The head geometry controls of the major factors influencing efficiency (power) of the engine: combustion pressure, and combustion geometry. The burning of fuel and air in the cylinder is basically a very fast chemical reaction. The laws governing speed of a reaction, imply a faster and more thorough burning of the fuel + air in the head, with a) more air velocity and b) more pressure=temperature=decrease in volume.
Quite simply put, the compression ratio creates a higher pressure in the cylinder when the spark plug fires, causing the flame to 'explode' with a lot more force, pushing down on the piston. This creates higher torque because of more force pushing on piston, but also requires more force to push the piston back up and compress the fuel air mix.
We calculate CR by taking the total volume (displacement plus head) and dividing that by the head volume alone. For a 70cc kit with a 7 cc head (stock 50cc) + gaskets ( 1-2 cc) it works out like (70+8)/8= 9.75:1.
PSI can be an indicator of compression ratio, but requires much tricker math to actually figure out CR. Other factors like ring sealing, port dimensions, pipes, intakes, etc, effect the PSI reading.
The 'squish band' affects the 'v' or velocity part of the equation. Air moving quickly has more energy and explodes faster. Imagine having a bowl of vinegar and dumping in baking soda. If you stir the heck out of it, it will fizz up much more violently. That is what is happening as the piston approaches the squish band. The quick decrease in volume will blast all the gasses into the hemispherical chamber around the spark plug at the same time, the violence of moving air speeds the reaction. Jennings and Bell reccomend the 40% of area- 7 deg taper method of sizing a squish band.
Because of the 'faster' flame in a high compression setup, ignition timing will have to be retarded. The ignition triggers and begins igniting the fumes before top dead center, to account for the time it takes to burn the air. When the everything burns faster, the max intensity of the explosion is at the wrong time and pushes the piston down as it comes up (knocking or pinging). This is exacerbated by a pipe, (or supercharger) which increases the pressure in the cylinder.
Sometimes the compression is just too high, the fuel ignightes without any spark, this is also problematic. Going to a higher octane fuel (only necessary in this condiditon) will allow you to continue to run the higher CR and pipe, otherwise you have to drop CR or go to a different pipe.
The 2 stroke gets more complicated also, because there is a huge hole (exhaust port) in the side of the cylinder. So even though on paper the compression ratio for identical 70cc cylinders, with different exhaust timings, will be the same, the holes in the side, and efficiency of exhaust porting will make their actual combustion pressure drastically different.
Finally, what are you looking for with your bike? The mods that mostly effect the final combustion pressure are: More aggressive intake porting= higher compression, more aggressive exhaust porting = lower compression, more radical pipe= higher compression at high rpm's when pipe hits.
If you switch to a higher compression head, and think you are detonating (sounds like rocks rattling in a can... and isn't your crankshaft) try to retard your timing a bit, see if your power improves. Some kits require so many base gaskets to clear a stock head, or small HC, that by the time all that gets put on there they actually have crummy compression, or a lack of bottom end from having all the ports shifted up. When the compression comes back, a bike that was tuned for different setup, can get thrown off. The detonating sound will be nastiest when you are really cramming on the pipe hard. If the timing doesn't fix it, and you're jetted correctly, and running premium gas and synthetic oil, then try putting in more head gaskets to drop compression a bit.
The cylinders that i've already made a lot of heads for (DR hobbit, MK65, and Polini) the compression ratios are just about figured out, but there is a lot of improvement for specific setups. Knowing what to look for makes it a lot easier to fine tune compression with head gaskets, and play with squishin' dynamics.