I've had insomnia most of my life and am an incredibly light sleeper (not helped by health issues) and the best thing I've found for cutting out background noise when it can't be avoided is silicone earplugs (the type you use for swimming), they are soft, pliable so easily inserted/removed and quickly warm up to body temperature so you forget they are installed (enough that I've made it to work a few times with them in).