We investigate the interaction of a fluctuating alpha-effect with large-scale shear in a simple 1-d dynamo wave model. We extend the calculations of Proctor (2007) to include spatial variation of the fluctuations, and find that there can be a mechanism for magnetic field generation, even when the mean alpha is zero, provided the spatiotemporal spectrum of the fluctuations has an appropriate form. We investigate dynamo action when the new term arising from the fluctuations is non-zero, and present results of the stability and parity of the system.