You will never banish the bunnies and dust completely. The dirt, fibers, hair and soot are here to stay; however, you can decrease the dust by adding humidity to your home.
A humidifier in your largest room or where there is the most activity usually helps. There are also humidifiers that can be added to your furnace/AC such as a water softener. They will not only control dust, but will make the environment more moist; thus a little better for itchy dry skin and that annoying shock you get every time something is touched.
I also use a microfiber cloth!

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