To clean Swiffer dusters, which I really like, simply swish the dirty duster in a sinkful of sudsy, warm water, rinse, and roll in a paper towel to blot out excess moisture. Reattach to handle, fluff, and allow to air dry. These are expensive refills to buy and you can use each one many times this way!
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After years of throwing out those "disposable" dusters, I threw one in the wash and was amazed to see it was not only clean as a whistle but reusable as well! To get the fluff back, I just gave it a few slaps against the top of my washer.