In rod-shaped Escherichia coli cells, the Min proteins, which are involved in division-site selection, oscillate from pole-to-pole. The homologs of the Min proteins from the round bacterium Neisseria gonorrhoeae also form a spatial oscillator when expressed in wild-type and round, rodA- mutants of E. coli, suggesting that the Min proteins form an oscillator in N. gonorrhoeae. Here we report that a numerical model for Min-protein oscillations in rod-shaped cells also produces oscillations in round cells (cocci). Our numerical results explain why the MinE-protein rings found in wild-type E. coli are absent in round mutants. In addition, we find that for round cells there is a minimum radius below which oscillations do not occur, and a maximum radius above which oscillations become mislocalized. Finally, we demonstrate that Min-protein oscillations can select the long axis in nearly round cells based solely on geometry, a potentially important factor in division-plane selection in cocci.