I use the same typ of "mop". It can actually be used wet or dry, and I take it off and rinse it out while washing my floor to make sure the pad is always clean. I have hardwood floors, so you can't use much water on them and this works awesome! I bought mine from WalMart, and also an extra pad. I use it on lino, hardwood and laminate and it works awesome on them all. I use the "regular" mop outside on the deck now!! Oh, and mine hasthe pockets on each end so the sleeves fit over the ends and it seems to stay on really well. My mom has a few and they are all velcro.....I've rolled them off a time or two! Maybe I scrub too hard?!?!
I also have the Swiffer with the pre wet pads, but I only use that when people are coming over as it smells good! But I'd rather not the chemical residue on the floor with the kids and pets.