Cognitive models of decision-making usually assume a noisy accumulation of evidence until a threshold is reached. The most commonly used model in this class is the Wiener diffusion model. This model assumes that noise in evidence accumulation follows a Gaussian distribution. In this talk, I will propose a similar model of decision making, but one that assumes "heavy-tailed" noise in the evidence accumulation, and thus replaces the diffusion process with a so-called Lévy flight. In this model, the shape of the noise distribution can be modelled by the additional stability parameter alpha. Thereby the diffusion model becomes hierarchically nested within the more general Lévy Flight model. Of particular interest is that the Lévy flight model contains an inherent mechanism to explain fast errors, which are often observed in perceptual decision making. I will present data from different tasks comparing the goodness-of-fit of the new Lévy-Flight model with that of the traditional diffusion model. Possible biases in parameter estimation arising when Lévy-Flight data are analyzed with a diffusion model are discussed.