First: are omelettes, classically anyway, supposed to have any browning on the outside? My hunch is that they're not, but I don't know for sure.
Second: I don't like my omelettes with a browned exterior (I think browning makes them tough), yet they insist on coming out browned or too runny. How can I prevent this? As I see it, my options are lowering the heat, putting the eggs in the pan while the butter is still foamy, or using a larger pan so that the eggs are dispersed widely, are thinner, and cook quickly. The Joy of Cooking says that cooking an omelette should be rapid and over high heat, so that makes me reluctant to do the first option, and the second is a direct contradiction of the omelette instructions in the JOC as well. I think the third option might work, but it could counteract the fluffiness factor I'm going for; how fluffy can a really thin omelette be?