I will say this and I will probably get blasted by a few, but saws generally do not start from a cold condition (truely cold....not been run in a day, cold) in two pulls. I have 30+ saws and the only ones that will start in two pulls are those with a primer. I got the Efco out the other day. It hasn't been run in weeks. I primed it and it popped on the second pull. But I believe it took a couple of pulls from there to start. The 346NE's are pretty good, but they usually don't pop until the third pull after priming. I have a 362 and it took about 6 pulls tonight to get it to pop. All of these saws are properly tuned and are running Ultra with stabilizer. Most saws are 4-6 pulls to pop. If they haven't been run in some time, it is not abnormal for it to take more pulls. This happens bc the fuel drains out of the carb when they sit. When you are pulling the starter you are priming the carb through the vacuum created by the piston pumping. Until the fuel gets back into the carb, it won't pop. Some older saws are real bears. My 125, though tuned well, with a good carb, requires priming by squirting mix directly into the carb. Once it is hot, it will start as you would expect. But if it sits more than a couple of hours, it is easier to just get the primer bottle out. It's kind of like starting a top-fueler.
Sham, what is your starting technique? It should be- 1) set the choke and pull until it pops--do not touch the throttle 2) when it pops, push the choke in and continue to pull until it starts---don't touch the throttle until it is running.