From a study of the intensity and polarization data of a large number of pulsars, Lyne and Manchester (1988) showed that pulsar beams are essentially circular in cross-section, and confirmed that pulse widths are inversely correlated with pulse period. Using a homogeneous sub-sample of 80 “cone-dominated” pulsars from their compilation, we find an inverse correlation between pulse width and radio luminosity. We conclude that pulsar beams become wider at lower luminosities. This effect is expected since pulse profiles are observed to fall-off smoothly at their edges, thus showing that pulsar beams do not have sharp edges. If beams do become wider at lower luminosities, then some of the dispersion in the observed pulsar luminosities is not intrinsic, but merely due to varying offsets of the line-of-sight from the beam center. In view of this, one should re-examine the usual procedure of independently modeling the luminosity and beaming in pulsar statistics calculations. We expect that a self-consistent approach that includes luminosity and beaming within a single model will indicate that the “effective” beam size for statistical calculations is significantly larger (by a factor ~2) than the size one usually estimates based on the observed sample of high-luminosity pulsars.