Thanks, bestyears, for your response. After I read it, I tested an old 3M ScotchBrite microfiber dust cloth on my foot-square sample of backsplash tile, which is exactly the same as my future floor tile, only smaller. This dust cloth will "catch" on my hands if my skin is dry and rough, but there was no problem with catching on my tile sample. It seems that the tile is heavily textured, but not rough to the touch as I had thought. So maybe the Bissell Steam Mop will work out after all. Thanks again!

We have a Karcher commercial German steam cleaner and compared to the cheaper models I've tried, it's really the bomb. Takes about 20min to heat up, but has a huge reservoir and can clean on full steam for about 2 hours. Comes with a zillion attachments for doing grout, stove interior, fridge, radiators, etc. It's also a very pretty yellow color. :) Pricey, but you can often find refurbished ones or look on eBay. I agree that floor cleaning really doesn't seem to have an inherently optimal procedure. You can use a Hoover type carpet shampooer on concrete, tile, or wood, but the ones I've seen don't seem to get very hot, certainly not to steaming -- they just kind of throw down warmish water and then suck it back up. (They do clean, but I don't think they do as good a job as a real steamer, and they do use a lot of water which isn't super for wooden floors.) You can use a steamer with lots and lots of washable pads, as we do. Or you can vacuum and then mop with 2 buckets. It's really a first-world problem, I suppose, but heck, floors have to get clean somehow and knees DO wear out. As cat owners we've appreciated our Karcher steam cleaner in preparation for visiting relatives who are allergic -- steam the floors and get a HEPA air filter going, and they don't even notice there are cats present.

I have the H2O steam mop with the ring. It does not remove stains but does refresh the carpets. All in all, I'm quite happy with the H2O. It does a great job of the rest of the floor surfaces. Laurel

This is the type of mop I have been using, and my brother ordered a replacement refill from Home Depot for about $7.00. I like this mop - until the sponge part disintegrates, which happens very quickly if I try to scrub the floors. Therefore I ordered some diaper pins to use to secure a microfiber cloth (we have lots of those) over the sponge, and I am hoping that that will keep the sponge intact. Changing shoes is a good idea, if I could store the patio shoes outdoors, but when it is 115°F/46°C outdoors, I'm afraid they would get too hot. I think it would be better if I could power wash the patio and get rid of the dirt/dust there, but I know it will come back quickly, in the next dust storm. Normally, I vacuum the patio with a leaf vacuum - mainly to pick up stray leaves and prevent them from getting into the pool, but this does not pick up all of the dust, and I have to do this early in the morning, when it is only 90°F/32°C, but this means that I have to do it before 8:30AM. I'm not all that good at cleaning that early. In the house, I do have a sort of hand vacuum that I use, but it is the type that you have to carry with a strap on your shoulder, which makes it more maneuverable but still a workout. I have found that the dirt that gets on my tile floor does not come off easily with a mop and needs to be scrubbed. I need a good scrubbing mop - and one that is durable. I'm looking at this one, but it is almost $40. ETA: I am unable to paste text or links when on GW, and so I had to switch temporarily to Houzz, which I really dislike.