It sounds like your body could be taking time to get used to the lower levels. But have you had your other bloods checked recently (thyroid, full blood count etc)? If these are off balance they will also affect your bs control, sleep and alsorts. Probably worth going to the doc for a general MOT to make sure it's not something unrelated to diabetes. I don't sleep well if bs is 5 or less, even though I'm used to this level during the day, but it doesn't make me feel like you describe.
Going down from 8 to 4 overnight isn't good. You'd be better setting your dose to keep you level overnight, then (once any other factors have been ruled out) gradually bringing the bedtime reading down a bit.