Don't try to run away from it, the more you'll try to hide it and be ashamed of it the worse it could get. So don't wait for your stutter to "disappear on its own", it'll just put you in a denial. I also support the speech therapy idea. Also, it is said, that adrenaline blocks dopamine which is responsible for stuttering so here's one idea why you don't stutter in those situations, I personally think that in some of those "high demanding situations", physically or socially we're actually able to stop thinking about how we'll perform and take all our attention to what we need to say. Fight wins against flight. On the less demanding situations all our hidden subconscious beliefs that could've formed our stuttering start creeping in. It's no life seeking for adrenaline to eliminate your stutter, so seek for speech therapy instead.