Maybe you just need a new mop system? having tried all the shitty swifer, shark steam mops and shit, i just broke down and got this
Amazon.com - Mopnado Foldable Spin Mop LIME Compact design folds up to 10 cube now includes bonus Scrub Brush - Wet Mops
a mopnado. It's the kind where you push up and down and it spins it dry and wet. You don't have to vigorously go up and down, really just 3 strokes is all you need. I've come to like these frilly microfiber mop heads, over the flat piece of swifer cloth, one time a glass fell and shatter, the mop was able to pick up everything.
It folds up nicely into a "box" so it saves space and you can stack a few things on top of it (wouldn't stack heavy shit of course). It's more expensive than the other spin type mops, but those other reviews complain about the mop heads breaking or the handle bending (this is steal, it's pretty strong) or the spin device not spinning anymore. I bought it about 2 years ago, it works nice, fuck i even learned you can sorta clean carpets by mopping, just dry vac and a light bit of water to get some of the surface dirt off.
I clean the microfiber mopheads in their own little bucket with a bit of bleach (i don't like throwing them in with my laundry, that's just nasty, wtf, who does that?) mopheads are like 8bucks.
For years, i like everyone started out with the bucket mop, some crappy device to "wring" out the water, mop horribly dunk it back into the bucket and "wring" again. Then you use a swifer and your like, oh this works sorta fine, then it's annoying when you just can't seem to get a good clean out of it. steam mop seems to take forever to "go over the area slow" but it works.
Just a good ol fashioned mop, and put some elbow grease it, actually finish faster too.