We have some sheet clips that slide over the sheet and rope/ribbing on the mattress edge. They are easy to put on when you 1st make up the bed and keep the sheet tight as a drum. I've not seen them for years...I think we bought one set at bed bath and beyond but I'd check online places too like Amazon or Ebay.
If you sew at all you can redo one end to make the sheet shorter. But I use the clips no matter if the sheets fit or not...I also hate wrinkled sheets.
I just checked Amazon.com...type in sheet grippers...they have 2 different ones. I put them on the lower/close to the platform edge of the mattress over the sheet. It take a bit of practice to get them over the cording but once you get the technique down it's fairly easy. You can buy enough sets to put on all 4 sides (2 per side) if you want to. good luck!