Stimulus selectivity of sensory systems is often characterized by analyzing response-conditioned stimulus ensembles. However, in many cases these response-triggered stimulus sets have structure that is more complex than assumed. If not taken into account, when present it will bias the estimates of many simple statistics, and distort the estimated stimulus selectivity of a neural sensory system. We present an approach that mitigates these problems by modeling some of the response-conditioned stimulus structure as being generated by a set of transformations acting on a simple stimulus distribution. This approach corrects the estimates of key statistics and counters biases introduced by the transformations. In cases involving temporal spike jitter or spatial jitter of images, the main observed effects of transformations are blurring of the conditional mean and introduction of artefacts in the spectral decomposition of the conditional covariance matrix. We illustrate this approach by analyzing and correcting a set of model stimuli perturbed by temporal and spatial jitter. We apply the approach to neurophysiological data from the cricket cercal sensory system to correct the effects of temporal jitter.