MACHO Project photometry of 45 LMC first and second overtone (FO and SO, respectively) beat Cepheids that pulsate in the FO and SO has been analyzed to determine the light-curve characteristics for the SO mode of Cepheid pulsation. We predict that singly periodic SO Cepheids will have nearly sinusoidal light curves; that we will only be able to discern SO Cepheids from fundamental (F) and FO Cepheids for P≲1.4 days; and that the SO distribution will overlap the short-period edge of the LMC FO Cepheid period-luminosity relation (when both are plotted as a function of photometric period). We also report the discovery of one SO Cepheid candidate, MACHO*05:03:39.6-70:04:32, with a photometric period of 0.775961±0.000019 days and an instrumental amplitude of 0.047±0.009 mag in V.