It sounds like your Insultard is peaking during the night, and you are running out of insulin by the following evening. Lantus or Levimer should help flatten things out. That certainly was my experience when I switched from NPH to Lantus. But to get it to work properly, I needed to split the dose between bedtime and morning shots. With me, it doesn't last the full 24 hours. As always, it is a case of test-and-measure until you find what works best.
Lantus and Levimer are both good basal insulins. I haven't used Levimer - Lantus works fine for me. But according to the research nurse who was doing clinical trials at the local clinic, you need larger doses of Levimer and you are more likely to need two shots a day.