Better than a comp terst is a leakdown test, an engine with a good compression might suffer from porous block syndrome, a cracked block around the liner that only leaks with the coolant hot (under pressure) as the engine is switched off. If one piston is clean when you do the head that's what it is.
Also look for leaking core plugs, weeping radiator, the multitude of hose clamps and the bottom of the plenum on an EFi, plus damp carpets.
Does it misfire when you start from cold at all?
