Magnetic resonance imaging (MRI) has become a key technique in the study of multiple sclerosis. In a typical analysis pipeline binary lesion maps are typically modelled voxelwise using either standard linear models or logistic regression, in order to detect relationships with variables of interest. Fitting linear models does not respect the binary nature of the data and, as we shall show, this can lead to false positives. Instead voxelwise logistic regression correctly models the data however it suffers from a lack of power. Smoothing is a key means of increasing the signal to noise ratio in neuroimaging data but has previously been thought not to be applicable to lesion based logistic regression as, when applied to the 0/1 maps, it destroys the binary nature of the data [9]. In this work we show how to combine smoothing with logistic regression modelling: increasing the power of inference whilst maintaining validity. In particular we develop a test based on sign-flipping the smooth effective score contributions and control for multiple testing using the sign-flipped distribution of the maximum smoothed score test-statistic.