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To my understanding, it isn't so much a added compression that gains efficiency as it is added expansion one gets with a higher static compression ratio - the added compression is really an unwanted side effect. In a gasoline engine you might run a static compression ratio of, say, 16:1, but leave the intake valves open for part of the intake stroke, so part of the charge is pushed back out. For the rest of the cycle it operates with a 16:1 ratio, just with lower cylinder pressures, much like if you were limited to only 3/4 throttle but without the throttle plate pumping losses.
If cylinder pressures weren't limited this way, early detonation of the combustion charge would be inevitable with such high compression (without super high octane fuels), and in most engines that can cause damage and negative work.
Diesels operate solely on detonation. To my knowledge, many already have compression ratios as high as 20:1 and have no need for limiting cylinder pressures. I'm less familiar with how engineers optimize them though.
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