In stage III hypopharyngeal cancer the tumor is (1) found only in one area of the hypopharynx and is 2 centimeters or smaller; cancer has also spread to a single lymph node on the same side of the neck and the lymph node is 3 centimeters or smaller; or (2) in more than one area of the hypopharynx, is in nearby tissues, or is larger than 2 centimeters but not larger than 4 centimeters and is not in the larynx; cancer has also spread to a single lymph node on the same side of the neck and the lymph node is 3 centimeters or smaller; or (3) larger than 4 centimeters or has spread to the larynx; cancer may have spread to a single lymph node on the same side of the neck and the lymph node is 3 centimeters or smaller.