3-Stroke Engine

Take a diesel 2-stroke, with intake ports at the bottoms of the cylinders and exhaust valves at the top, add passages from the exhaust valves to another cylinder (also valved for reasons that will become obvious). Second bank of cylinders have valves coming from first bank and a second set of valves going to exhaust. The two cylinder banks are synchronized by gears, or whatever else, so that each cylinder in one bank moves in sequence the same cylinder in the other bank.

A supercharger pushes air into cylinder at BDC, piston compresses air, diesel is injected, and *bang*, just like any other diesel 2-stroke.

Here's where it's different -- exhaust valve opens to other cylinder immediately, allowing twice as much (or whatever, depending on second cylinder's size) expansion for higher efficiency. Leave exhaust ports open long enough to evacuate cylinder #1 and close again. While fresh air is compressing in cylinder #1, secondary exhaust valve in cylinder #2 is opened, pushing remaining gasses out to the atmosphere. Close those right before *bang* in first cylinder and repeat...

Anyway, you might make the secondary expansion cylinders a little smaller. This kind of applies the ideas of Miller and Atkinson to two-stroke engines. I think it would be more efficient than a four-stroke (and probably better power to weight ratio), but I don't know how it would stack up against a Miller-cycle four-stroke.