In the convolutional retinex approach to image lightness processing, a captured image is processed by a centre/surround filter that is designed to mitigate the effects of shading (illumination gradients), which in turn compresses the dynamic range. Recently, an optimisation approach to convolutional retinex has been introduced that outputs a convolution filter that is optimal (in the least squares sense) when the shading and albedo autocorrelation statistics are known or can be estimated. Although the method uses closed-form expressions for the autocorrelation matrices, the optimal filter has so far been calculated numerically. In this paper, we parameterise the filter, and for a simple shading model we show that the optimal filter takes the form of a cosine function. This important finding suggests that, in general, the optimal filter shape directly depends upon the functional form assumed for the shadings.