The oblate spheroidal wavefunctions proposed by Rodríguez-Morales and Chávez-Cerda are shown to be possible representations of physical beams only when the angular function $S_{mn}(\beta ,\eta )$ has odd $n-m$ . This condition makes $S_{mn}$ odd in η, which ensures the convergence of integrals of physical quantities over a cross section of the beam. The odd $n-m$ condition also makes $S_{mn}(\beta ,\eta )$ zero in the focal plane $z=0$ outside the circle $\rho =b$ , and thus allows for the physically necessary discontinuity in phase at $z=0$ on the ellipsoidal surfaces of otherwise constant phase. Only a subset of the oblate spheroidal functions can be exact representations of nonparaxial scalar beams.