Grab one of these sets of three thick and thirsty reusable cloths made to fit a standard swiffer or other similar convenience mopping system and say goodbye to the disposable ones. (the kind where you shove a corner of the cloth down into the pokey hole to make it stay attached).
These cloths are made out of thick and highly textured cotton chenille fabric. These are just as good as the dry disposable mopping pads for dry dusting, but they really shine as a damp mop pad. Simply dampen the cloth with floor cleaner or soapy water or whatever you like to use, attach to your mop and go to town. Or, you can spray your cleaner right onto the floor and use the cloth to mop it dry.