Special-purpose constraint propagation algorithms (such as those for the element constraint) frequently make implicit use of short supports — by examining a subset of the variables, they can infer support for all other variables and values and save substantial work. However, to date general purpose propagation algorithms (such as GAC-Schema) rely upon supports involving all variables. We demonstrate how to employ short supports in a new general purpose propagation algorithm called ShortGAC. This works when provided with either an explicit list of allowed short tuples, or a function to calculate the next supporting short tuple. Empirical analyses demonstrate the efficiency of ShortGAC compared to other general-purpose propagation algorithms. In some cases ShortGAC even exhibits similar performance to special-purpose propagators.