Hello,
I can't comment on the insulin you are using, but I have had a similar problem with Levemir before. I was taking my full dosage (to last the 24hrs) before bed and finding I was suffering hypos around 4-5hrs later. These hypos were followed by a subsequent 'rebound high' in the morning.
I also found the Levemir didn't quite cover the full 24hr period even though it claims to.
To combat both the above issues; I split my dosage in half, injecting 12hrs apart. i.e. 10pm and 10am. This stopped the night hypos and also the rebound highs.
This worked for myself using Levemir but I wouldn't try this without first consulting your Dr. I also noticed that when I split my dosage I actually used less insulin. 40 units down to 36.
Hopefully someone else can add their experience.
Regards,
Grant