Abstract Phonological grammars characterise distinctions between relatively well-formed (unmarked) and relatively ill-formed (marked) phonological structures. We review evidence that markedness influences speech-error probabilities. Specifically, although errors result in unmarked as well as marked structures, there is a markedness asymmetry: errors are more likely to produce unmarked outcomes. We show that stochastic disruption to the computational mechanisms realising a Harmonic Grammar (HG) can account for the broad empirical patterns of speech errors. We demonstrate that our proposal can account for the general markedness asymmetry. We also develop methods for linking particular HG proposals to speech-error distributions, and illustrate these methods using a simple HG and a set of initial consonant errors in English.