Around here redwood is a little pricey to use for sleepers. :-) Definitely use pressure treated lumber for contact with concrete.

Nothing wrong with construction adhesive. I'd shim the sleepers as necessary and use something like Tapcons to keep things from moving around until the glue sets up.

Mike

I think you still want to nail them. There is a tool that does this, it actually uses gunpowder to shoot the nail into the concrete. Here is a snip from someone's blog:

"I bought a manual stud driver for $20. You put a special concrete nail into the end of the muzzle and then put in a special .22 caliber charge. Press the nail against the desired spot and hit the top of the nail driver with a hammer. The charge forces the nail right down into the concrete. This is a must-wear-ear-plugs tool. "

That sounds like what my ex did to attach the studs to the concrete walls when finishing a basement.
The process seemed to have a high level testosterone component ;)

Here's some more info:

"Choosing the Right Masonry Fastener

When attaching wood to masonry, you'll need special fasteners. You can choose from three basic types: hammered, powder-actuated, or shield-and-anchor.

Hammered fasteners are designed to be driven through furring and into masonry using a heavy hand-drilling hammer. These include spiral masonry nails and cut nails, which are heavy, flat, and tapered. Unfortunately, nails present a serious drawback: You don't have room for error when driving them. A glancing blow can loosen the nail. On the plus side, you don't have to predrill your masonry and furring strips, a requirement of shield-and-anchor systems.

Powder-actuated fasteners (PAFs) are pins that you shoot through the furring and into the masonry. This takes a special handheld tool that discharges a .22 caliber cartridge for each pin it drives; follow the manufacturer's instructions for use. (Use extreme caution--if a PAF is misused, the pin can act like a bullet.) PAFs work only with concrete, not bricks or cinder blocks. The charges come in several different sizes that are color-coded to match the strength of the concrete. Make sure you select a charge that neither overdrives the nail (through the furring strip) nor leaves the nailhead exposed. The nailhead should lie flush with or just below the furring's surface. (Experiment with different charges until you find the right one.) PAFs offer a twofold advantage--you can work very quickly, and you don't have to predrill the masonry and furring strips as you do when using a shield-and-anchor system.

Shield-and-anchor systems consist of two parts. You insert the tapered lead or plastic shields (expanding tubes) into predrilled holes in the masonry. When you drive the screws (matched to the shields) through the furring, they expand the shields, gripping the sides of the hole and resisting withdrawal."

Remington is one company that makes the powder actuated fasteners, if you decide to go that route. Just be sure to use the proper safety equipment. A misfired nail can do some serious damage.

Shimming pressure treated lumber is fine---as long as pressure treated or plastic shims are used.

As far as PAF--powder activated fasteners---goes, many areas require training to properly use those---there are several different loads---for long/short nails and different types of concrete----so to safely use them a bit of training is necessary.

Tapcon screws require a hammer drill---easily rented if the $70-$150 cost is too high. The learning curve for Tapcons is very short and the safety factor is very high, compared to PAF.

Construction adhesive combined with a Tapcon every three or four feet will usually be quite secure.

A: Construction adhesive (PL400) with no mechanical fasteners is more than adequate. Why tear up the concrete any more than you have to? Shimmed pressure treated is the way to go.

B: Sleepers on a concrete floor: sounds decidedly uncomfortable.

A: Construction adhesive is in no way adequate for the job.

paf's or tap cons are the only way to go.
OSHA requires that you be trained with a PAF before using

"OSHA requires that you be trained with a PAF before using"

Good thing this is a homeowner.
Hilti also makes powder actuated tools, and theres are in larger calibers (.25 & .27) and someone was making a .30).
Rent a Hilti gun if you can, they are much easier to use than the old hammer type.