You seem like a pretty smart guy, so I'll give you the technical version.
Draw is the result of a pressure differential caused by temperature difference. The volume of air in the flue is at a lower pressure then the cooler ambient air. This pressure differential drives the flues draw. The more air in the flue, the more draw. The hotter the air in the flue, the more draw. So, to increase draw you can increase the height leading to more volume, increase the flues cross section leading to more volume, or do something to increase the temperature of air in the flue like insulate it.
edited to add:
And of course by limiting anything in the flues design that will lead to friction loses, like drastic transitions, elbows, ext....