I learnt my lesson. The problematic molecule for which our NMR data was not making sense turned out to have some protons with really long relaxation times. I had read a line in some well known NMR book which said "For any detailed study, it's best to measure T1 relaxation times before the experiment". I read it, and I forgot it. Well, not forgot it entirely, but it's still true that for most molecules, relaxation times are similar for all the protons and not doing a T1 does not really make a difference. In our case unfortunately, it were the reference protons for the NOESY distance calculation that turned out to have loooong T1s. Simple solution: measure T1, and then set the relaxation delay (d1 for Varian spectrometers) equal to 5T1. I am in the process of rerunning the NOESY. But from next time, I am never going to forget doing a T1 measurement before anything else, even for simple and 'obvious' moelcules. It's a humbling lesson well learnt for me.