"Chemicals rarely clear a stoppage—they only make a small hole," says TOH plumbing and heating expert Richard Trethewey. "A full stoppage requires mechanical clearing." Remove the stopper and block off overflow holes. With water in the bowl—the water puts more pressure on the clog—plunge with a flat-faced plunger. If that's not enough, get under the sink and take off the trap to see if that's where the clog is lodged. If the blockage is deeper, rent yourself a hand snake. Slowly push the coil down the drain, carefully twisting, pulling, and pushing when you hit the blockage. If the snake fails, then the still waters truly run deep. Call a drain-clearing service to get things flowing.
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