A.Van Perrine, of U.S. Gypsum Co., responds: Compared with an unpainted drywall surface, a painted surface has essentially been "sealed." The compound contains air that has to escape as it dries. With unpainted drywall, the air can escape both through the drywall surface and out into the air. When the drywall is sealed with paint, all the air has to escape outward, and it tends to create the small air bubbles you mention. There’s nothing you can do but add successive thin skim coats of compound and lightly sand between coats until smooth.
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