We consider the goals of the introductory course in classical mechanics taken by physics majors and argue both that these goals are not well met in actual courses and that the goals themselves should be rethought. We propose alternative goals and describe an introductory “modern mechanics” course that addresses these alternative goals. Included in the description are several genres of homework problems that are nearly absent from traditional mechanics courses at both the introductory and intermediate levels. The intermediate mechanics course could be restructured to exploit a broader foundation laid by the introductory course.