I have a Don Aslett Mop. It has a microfiber cloth pad for dusting or mopping the floor. The pad is affixed with a row of velcro on the bottom of the mop.
Instead of using the pads that came with it, I like to use my own crocheted rectangle. I make it several inches larger than the mop head, all the way around. It doesn’t have to be fancy, just a regular crocheted (or knitted) rectangle will do. The yarn sticks beautifully to the Velcro on the bottom of the rectangle mop and they can be easily thrown into the washer to use over and over.
Because it is crocheted several extra inches all the way around, it makes a big buffer to protect the baseboards and the larger amount of yarn helps the job get done faster. The yarn also has a good texture to help scrub places on the floor that need a little extra scrubbing.