The Bredt rule, which proved useful in earlier decades mainly as an exclusion criterion in the assignment of structures, has in recent years become the stimulus for efforts to synthesize strained bicyclic systems with a bridgehead double bond. On the basis of the ring-strain forces operating in such systems, an extended Bredt rule is discussed. The "Bredt compounds" to which this rule applies, which include bicyclic systems not previously considered from this point of view (e. g. bridged methylenecyclopropanes), form a clearly circumscribed, interesting field within the chemistry of highly-strained hydrocarbons with ring unsaturation.