Thin air mattress

I've been looking about for a thin air mattress, about 4-5" thick without much luck. My coach sofa folds down and is padded, but is uncomfortable and lumpy because of the seams in the cushions. I was looking for something that could be folded to take up very little space between uses, thus a mattress topper or some such is not an option.

Does anyone have any suggestions? The one fairly thin one that I found on Amazon says 1-2 months shipping time, which doesn't sound very promising. Nobody else seems to have that exact model.

Thanks!