Suspended ceiling lighting, strapping in the way

For reasons I won't get into, my drywall ceiling in the basement had to come down and I'm replacing it with a suspended ceiling with 2x2 tiles.
I'm planning the recessed lighting cans, and no matter how I shift the t-bar grid around there's going to be some places where a piece of the 1x3 strapping running between the trusses goes right through the centre of the tile. And because I'm anal, I would rather the lighting cans be centred in the tiles.

So, my question is, can I remove a section of the strapping (NOT the trusses obviously) to put the cans where I want, and then screw some new 1x3 strips into the trusses, on either side of the can? Is the strapping providing much lateral support for trusses?

I could have some of the cans off-centre in the tile, but that's really going to bug me..

Thanks!

 

The 1x3 is not structural, it's a Canada thing... and is only there as backing for the drywall. Structural lateral support would never be a 1x, it would be 2x and would be located on the vertical webs of the floor trusses. Remove 1x3 and put it wherever you want.

 

I agree. Normally when the sheetrock is pulled.... so is the strapping. The new ceiling grid is hung directly from the bottom of the floor joists.

 

Awesome, thanks guys, I appreciate it!