I would like to build a deck over my concrete patio but the problem is I have only about 4 1/2 inches between between slab and top of concrete house slab. Therefore, I can only use 2x4s for supporting the low profile deck. All deck do it yourself books recommend a minimum 2x6 for deck joists. Is this a bad idea? Or can I use 2x4s to structure the deck? I assume the concrete patio can offer some support, but a portion of the deck would not be over existing patio. Any help would be appreciated.

My decking (an area of 13 ft x 25ft) is on 4" x 2" or the metric equivalent and is fine. I put the support beams every 3 ft and there is no warping or bounce when you walk on it. Approximately 6" off the ground.

Span is everything when it comes to joists. 2 x 4's setting directly on the concrete or shimmed as needed will be fine. How far are you going past the patio? If only a few feet, the 2 x 4's should still be fine. If further, you could scab on a second one or a 2 X 6. You might want to look into landscape timbers. Most wood for the buck.