The degree of cyclic conjugation in the 6-membered rings of phenylenes is shown to obey a rule that is related to Clar's aromatic sextet theory, and is, in a certain sense, inverse to it. If the hexagonal squeeze of a phenylene is an all-benzenoid hydrocarbon, then the cyclic conjugation in the 6-membered rings of the phenylene, corresponding to ‘full’ hexagons of the squeeze, is weak. Strong cyclic conjugation is found in the rings corresponding to ‘empty’ hexagons of the squeeze.