Linear alpha(2)Omega-dynamo waves are investigated in a thin turbulent, differentially rotating convective stellar shell. A simplified one-dimensional model is considered and an asymptotic solution constructed based on the small aspect ratio of the shell. In a previous paper Griffiths et al. ( Griffiths, G. L., Bassom, A. P., Soward, A. M. and Kuzanyan, K. M., Nonlinear alpha(2)Omega-dynamo waves in stellar shells, Geophys. Astrophys. Fluid Dynam., 2001, 94, 85-133) considered the modulation of dynamo waves, linked to a latitudinal-dependent local alpha-effect and radial gradient of the zonal shear flow. These effects are measured at latitude theta by the magnetic Reynolds numbers R(alpha)f(theta) and R(Omega)g(theta). The modulated Parker wave, which propagates towards the equator, is localised at some mid-latitude theta(p) under a Gaussian envelope. In this article, we include the influence of a latitudinal-dependent zonal flow possessing angular velocity Omega(*)(theta) and consider the possibility of non-axisymmetric dynamo waves with azimuthal wave number m. We find that the critical dynamo number D-c = RalphaROmega is minimised by axisymmetric modes in the alpha Omega-limit (R-alpha -> 0). On the other hand, when R-alpha not equal 0 there may exist a band of wave numbers 0 < m < m(dagger) for which the non-axisymmetric modes have a smaller D-c than in the axisymmetric case. Here my is regarded as a continuous function of R-alpha with the property m(dagger) -> 0 as R-alpha -> 0 and the band is only non-empty when m dagger > 1, which happens for sufficiently large R-alpha. The preference for non-axisymmetric modes is possible because the wind-up of the non-axisymmetric structures can be compensated by phase mixing inherent to the alpha(2)Omega-dynamo. For parameter values resembling solar conditions, the Parker wave of maximum dynamo activity at latitude Omega(p) not only propagates equatorwards but also westwards relative to the local angular velocity Omega(*)(theta(p)). Since the critical dynamo number D-c = RalphaROmega is O(1) for small R-alpha, the condition m(dagger) > 1 for non-axisymmetric mode preference imposes an upper limit on the size of vertical bar d Omega(*)/d theta vertical bar.