Well rest won't resolve the problem, you need to reduce your basal further. Going to bed on a bg level of 4 isn't ideal as it doesn't leave much margin of error if your bg levels drop during the night, once you do get your dose right you should be able to go to bed with levels of 5.5mmol but the choice is yours, try another reduction and see how you get on.
Noblehead makes a very good point.
A level of 4 when retiring for the night is far too low. I tend to ensure mine are around 8 when going to bed, which allows a drop safely if it should happen.
The advice you've got on this forum is excellent. As mo1905 says, also look at the insulin that you take at teatime as this will have an effect on your readings during the night and in the morning.
Have you also considered applying to go on a BERTIE course or DAPHNE course?
I know there has been some negative views posted about these courses, but the BERTIE course I attended in 2011 was most helpful with Trainers who gave you the respect and acknowledgement that you are the expert, not them.
I would recommend it.