I am having my baserment finished. I have had French drains installed with battery back up. Contractor installed vapor barrier, mastic basement floor, #15 paper put on top of that , more mastic and then plastic on top of that. Sleepers (2x4) exterier treated lumber with exterior 3/4 treated (b/c) on top as sub floor. Will put wood or an other covering on top of that to finish. My question. Sleepers are flooting. When I walk on plywood floor, a number of areas flex, bounce. When brought to attention of contractor, he said floor needs time to settle. Bounce will disappear. He said he did put shims under some 2x4 to level floor. Keeps telling me, nothing to worry about. IS HE CORRECT? Or do I have something to be concerned about?

In my experience with sleepers and their 'settling' it doesn't happen.

Now IF! And I say IF you put furniture on top,or say a pool table,then the floor will settle down just fine,constant and consistent pressure will make it lay down properly,but notoriously,treated lumber,be it either the sleepers or the plywood,will warp.

The plywood installed most likely was pre-warped before it was even installed.Am I right?

The shims installed had better have been treated as well,as the whole reason behind the treated subfloor and sleepers was for high moisture areas,right?So the shims,if they were only standard pine,or even cedar,will rot long before the sleepers will.

Hardwood shims would last longer,but even they will rot if the moisture content is high.(although hardwood shims would not have the compression problems that pine and cedar have,especially where moisture is concerned.)

If you are planning on having weight on this floor,other than just the new flooring(carpet/wood/etc)you might be just fine.. otherwise,I would suggest shooting Tapcon screws through the 'soft' areas,filling the holes with silicone sealer before the screws are buried so any moisture from below grade doesn't wick up through the holes.