Mine is new but not "just a leaf". It has a rubberized backing that prevents it from moving like a leaf. It has a sewn on hood that fits over the headrest which also keeps it from moving. The fabric is not cotton; it is made to absorb sweat/liquids. Strategic button placement keeps it in the seat. I spoke to the company before purchasing because the primary goal is to keep the Arizona heat down on leather seats. Alex gave me a study of the fabric and told me how it was tested for this purpose. (The test was to boil them in water to see if the rubberized base melted. That didn't happen!) While they're a little pricey, they're researched, designed, and well made. Their ease of use (in and out of the seat) is what sets them apart and why I ordered them and nothing else.
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