I recently went through this exercise: (ended up being a blown head gasket - but there are different blowout scenarios that behave differently - and I did not have a compression-tester).
My ALH never had white smoke coming out of the exhaust. It actually pretty much ran fine, and for several months, would take 10-15 mile drives on a daily basis, but if you drove it on the freeway, it would overheat. This was apparently triggered by a low-coolant episode caused by a leak in the radiator return hose. (or, possibly, after the leak was repaired, the car was driven with too-dilute coolant, because the lost coolant was replaced with distilled water; which makes it boil at a lower temperature, and also degrades the viton in the MLS head gasket).
Coolant leaks can be traced (even EGR leaks) with a fluorescent tracer dye. If it is ingested in the EGR valve, you should see trace in the intake downstream from the EGR with a UV light. If there are leaks anywhere else: fluorescent tracer dye will reveal it. (unless it's coming in through the water-jacket and head-gasket; I don't think there's a practical way to look in there if there's even trace visible). Though, when I took my EGR cooler off, I looked at it, and couldn't really imagine how that could develop a leak, it's a pretty sturdy and solid piece of hardware. (and very, expensive to replace). I used my mighty-vac, and rigged a sprinkler fitting, and just plugged the other end with my finger; and it held vacuum, so I figured that meant it was airtight.
If you see bubbles in your coolant reservoir coming from the coolant return hose, or soot, or if the coolant system is pressurized after sitting overnight, or if the pressure relief valve in the expansion tank getting tripped and level going up, any of those mean that you've got a blown head gasket. If your expansion tank is overflowing, then you'll see coolant on the ground under the car behind the front-right tire just generally dripping from the frame. (for me, it was actually kind of hard to figure out where this was coming from until I got the dye - but in retrospect, looking at the expansion tank being filled; it was obvious).
White-smoke has already been covered; so here's the thing about whether the white smoke is fuel, or coolant:
If it is fuel, this could be the result of a blocked intake, and you can rule out two pretty common causes.
That could either be build-up of soot in the intake, (which has also been covered), OR, a broken EGR cut-off butterfly; the little plastic vacuum actuator on the back of the EGR is pretty fragile, and commonly breaks, and if the arm is broken, then the butterfly valve can kind of flop loose. You'd see that immediately if you took off the intake hose. If it's closed, you'd get really crappy power, and white smoke that smells terrible. There is a lever on the back of the EGR assembly that you can control with your finger (if that plastic arm is broken, or disconnected).
So that's easy to rule-out. I thought I'd mention it. And unburnt diesel is really stinky.