Low-Profile Sofa Sleeper Sheet Set. Exclusively Made 200-Thread Count Sheet Sets. 5-inch Profile Fits Sofa Bed Mattresses We realized there was a huge gap in the sheets that we were providing. We offer wonderful sofa sleeper mattresses made from latex, memory foam and the Air Dream air-over-coil, but we did not have any sheets sets that truly fit these mattresses Now available in 200TC fitted sofa sleeper sizes By partnering with Gotcha Covered, one of the best producers of sheets and bedding, we can offer exclusive sheet sizes that will properly fit your sofa sleeper mattress or air dream air-coil mattress Available 200 ct Sofa Sleeper Sheet Sizes:. 4.5 inch depth sofa mattress profile. Full Size: (54 x 72 x 4.5 inch). Queen Size: (60 x 72 x 4.5 inch). Available Color: White/Ivory 200 Thread Count. The exclusive source for sofa sleeper depth fitted sheet sets. We are the only place where you can find these sheets. If you want sheets that will properly fit your 4.5 inch profile sofa sleeper mattress, then you need to get these sheets. With our sofa sleeper sheet sets, your fitted sheet will look like a correctly fitted sheet on your fold out sofa bed.