Detergents contain conditioners and brighteners and water softeners and other gunk that leave a lot of residue. Instructions for washing down items all say to run the machine empty for a couple of cycles to remove detergent residue and then use a special down washing product.

Henry Shires probably should change his website; Woolite is now a detergent formula, no longer a soap. At least so I have been told by a number of sources, including Woolite's own website.

Whatever you use, do a lot of rinsing! Soap can leave residue especially in hard water. I think the wet cloth idea followed by rinsing is the best.
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May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey