One variable apparently is the height of the pot above the stove flame - too close and the flame is cooled, creating CO. A blue flame is good, a yellow flame (usually incomplete combustion) is not so good.
Spot on. I have a research report (in Norwegian) where CO production for different kind of stoves were tested with and without pots for snow melting. CO production when melting snow was sky high, but with HUGE variations from stove to stove. CO production without a pot was consistently much lower.
The consensus at a outdoors enthusiast I visit is that the distance from the flames to the cold pot is the most crucial factor in CO production. It makes sense, but I have to re-read the report to see if it actually says so, or if that's the conclusion people have drawn.