For 'non-slick' covers I use packing tape which I 'desticky' some and then apply to the surface to lift dirt. If the tape is still too sticky your cover gets trashed! I would try "Post-It" notes on really valuable non-shiny covers.
For 'shiny' covers I use Maguires Scratch-X rubbed into a paper towel, then applied by rubbing the towel on the LP cover surface.
For splits om the edges, best practice is to leave them alone, and store the LP outside the jacket with both in a clear plastic sleeve.
For 'shiny' covers I use Maguires Scratch-X rubbed into a paper towel, then applied by rubbing the towel on the LP cover surface.
For splits om the edges, best practice is to leave them alone, and store the LP outside the jacket with both in a clear plastic sleeve.

