Classical theories of punishment and sociological conceptions of norms suggest two possible criteria: the perceived frequency and seriousness of offenses. Data from four independent sample surveys of the adult residents of a southwestern metropolitan area are used to determine the effects of these 2 variables on the severity of preferred punishments for 19 offenses. When the age and prior record of the offender are held constant, the seriousness of the offense is the central criterion used to determine appropriate punishments. These results cast serious doubts on recent claims that publicly preferred punishments are based on utilitarian motives. Study data and 23 references are supplied. (Author abstract modified)