Warning! Thread derailment!
I've actually been thinking a lot about a Brayton-like design.
1. It can have a smaller compressor piston than the combustion piston (an atkinson cycle)
2. If used with more than one compressor piston (starting large and getting smaller), or a turbo or supercharger, the charge can be intercooled up until the last compressor piston (miller cycle).
3. Between the compressor piston and combustion piston the charge could be fed through a heat exchanger that preheats and expands the charge before combustion (perhaps would work best on a diesel cycle or some other sort of stratisfied charge).
This would basically be similar to this type of turbine engine, but in piston form:
