This article presents a new procedure for constructing legislative district maps. This straightforward, transparent procedure is intended to be helpful to those interested in promoting fair, nonpartisan legislative district maps. The work draws upon a recent award-winning study of compact legislative districts. That study found that redistricting experts and lay citizens alike viewed districts that appeared to be square as most compact. The map drawing procedure combines compact districts with the well-established concept of partisan symmetry to build maps that are fair to both major political parties. The article opens by discussing this new view of compact districts and describes the procedure for constructing the maps. Maps with compact districts are drawn for 12 states that have recently been under court scrutiny. Partisan symmetry is then applied to these maps to construct legislative district maps that are fair and square.