We get good results with this product: http://en.fr.hg.eu/products/show/id/1112/plastic_garden_furniture_restorer
Simplest method would be to first use a vacuum brush or soft, dry cloth to wipe or brush off the inside and outside of the lampshade. Remember to remove all non-washable trim from the lampshade. Now filla bathtub with warm water and add laundry detergent. Soak the lamp shade in the soapy water and use some suds on a cloth or soft brush to lightly rub out soiled spots. swish the shade in the water.
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