I just had the squeezy things on my legs in the hospital. I didn't have any compression socks at home.
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I just had them on during surgery, they must have been taken off while I was in the recovery room because once I was moved to my regular hospital room they were off. I had on normal non-skid socks after. I was up and walking around within a few hours though, most have you take them off once you are moving. I think if you're at higher risk for blood clots they may have you wear them longer (clotting disorders, heart issues, over a certain age, level of activity, etc).