A.Ron Webber, a veteran plastering contractor in Orange, Calif., responds: With the right preparation — including a proper drainage plane and flashing — three-coat stucco should keep 99 percent of the water out of a building; any incidental water that does get in behind the stucco should find a way out, typically through the perforated weep screed at the base of the stucco rather than through holes made by fasteners penetrating the drainage plane. In my experience, it's much more likely that the windows and other penetrations are leaking than the stucco itself.
But before jumping to any conclusions, do some water testing. At the window that seems to be the leakiest, mask off the stucco by taping poly sheeting to the window frame, leaving only the window exposed. Then let water run against the window, allowing the tracks in the frame to fill with water while observing from the inside. If you haven't...
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