I've tried out a bunch of tire combinations, including regular road tires, road tires with tuffy liners, kevlar belted tires with and without tuffy liners (or with 2 tire liners!), and the semi-knobby tires you see on cheap MTB style bikes.

The semi-knobby tires are the ones that keep the tube the largest distance from the pavement (tread depth plus casing is about 8mm) even compared to running road tires with more than one tire liner.

From all this experimenting I've found that the way to completely avoid wire fragment and glass shard punctures is to have the tube further away from the pavement than the length of the piece of wire or glass. kevlar casings or hard plastic liners helped a little but tire thickness or tread thickness really prevented me from getting flats.

EDIT: I have also had most of my flats on rainy days. I have a hard time figuring out why that is true (the idea of water acting as a lubricant and thereby causing more flats doesn't seem like a great explanation to me, because even if water makes it possible for slivers of glass/wire to slide through the rubber a bit better, it seems the water would also make the things more likely to slip off of the tire.