Domains of simultaneous linear instability of first and second overtones in the Petersen diagram. Black dots represent the observed LMC double-overtone Cepheids. Line segments are models with normal and artificially increased luminosity, as described in the bottom panel. Asterisks and pentagons mark resonances between low order modes. Resonances might be helping to produce double-overtone behaviour only for the shorter-period Cepheids, but not for the more numerous longer-period ones.