Framing x Insulation boards

[Rod75]

I was looking at 2" XPS insulation and found that framing with 2x2, strips are not as thick as the insulation board and the 2x3 are a bit too high for framing. What have y guys used?

I'm doing a semi floating floor. Only frame on few spots, but still need to have same thickness with XPS boards.
Thanks y'all

[musigenesis]

I use 2x3s (and 1x3s in places) ripped to 2" (2x3s are actually 1.5"x2.5", so after ripping 1/2" they're 1.5"x2"). Easy to do with a table saw and not that hard to do with a circular saw and a steady hand.

[RamRod4]

For subfloor insulation and installation a lot of people use 3/4" thick furring strips screwed to the floor in a grid-like pattern. Preferably 48"x96" center to center. This allows for 3/4" thick foam board to be installed and then subfloor over top.

I chose to glue the foam directly to my painted steel floor and then screw down the subfloor through the foam with no furring strips underneath. The foam is rated to handle the load when spread out over the entire sheet of plywood.

From my research, 2" foam is excessive for a floor when you look at the gain in r-value its minimal. Not to mention the loss of ceiling height if youre not doing a roof raise. Same goes for the walls. 2" isn't worth the trouble or loss of space. 1.5" for the walls would be more ideal since most people frame out their exterior walls with 2x4's laid on their side (opposite the way a normal stud wall is framed). This leaves you with a 1.5" deep cavity to fill with foam board.

[Rod75]

Ripping all the strips is the solution I was trying to avoid. I might have to go with 1.5".
Thanks guys