I've been in quite detailed email conversations with two potential PhD supervisors, both of whom I've met in person. Both offering great projects for different reasons. I'd be enthusiastic to do either - but obviously can't do both. Also its obligatory to apply to more than one place just because the chance of being accepted anyway is not 1. But suppose I were to get both, how would I go about politely declining one? I imagine this must happen quite frequently, I don't want to go about offending potential future colleagues especially if I know them personally. My instinct is Profs and Drs are not easily bothered by this?