We present new, near-aphelion, time series of photometry of Comet 2P/Encke in Cousins-R band. With these light curves we find that the dominant, synodic rotational periodicity is either P0 = 11:079 0:009 hours or 2P0 = 22:158 0:012 hours. This is in contrast to data from the 1980s published by others that are consistent with 15.08- and 22.6-hour periods. Those periods do not satisfy our phased light curves, and also the 1980s data are not easily reconciled with our periods. This could be due to P/Encke having non-principal axis rotation or due to a drift in the rotation period caused by outgassing torques. We observed the comet at ve epochs: July, August, September, and October 2001, and September 2002, and the comet was at times intrinsically brighter than expected for a bare nucleus, due to an apparent contribution from an unresolved coma. Three-quarters of the data were obtained in the second and fth epochs, and we analyzed these two time series using both the phasedispersion minimization and "WindowCLEAN" techniques. At both epochs and with both techniques strong periodicities were found near frequencies f0 = 2:16 d1 and f1 = 4:35 d1. By then using visual inspection of the phased light curves to corroborate these frequencies, and by using the data from the other three epochs to properly align light curve features, we were able to derive P0 and 2P0 as the only solutions that satisfy all our observations. The periodicity due to f1 is clearly seen in our data, but we cannot tell from our data alone whether it is a manifestation of the nucleus's shape, non-principal axis rotation, or both.