Experiments and field trials have shown that the intracellular bacterium Wolbachia may be introduced into populations of the mosquito Aedes aegypti, the primary vector for dengue fever. In the absence of Wolbachia, a mosquito acquiring the dengue virus from an infected human enters an exposed (infected but not infectious) period before becoming infectious itself. A Wolbachia-infected mosquito that acquires dengue (i) may have a reduced lifespan, so that it is less likely to survive the exposed period and become infectious, and (ii) may have a reduced ability to transmit dengue, even if it has survived the exposed period. Wolbachia introduction has therefore been suggested as a potential dengue control measure. We set up a mathematical model for the system to investigate this suggestion and to evaluate the desirable properties of the Wolbachia strain to be introduced. We show that Wolbachia has excellent potential for dengue control in areas where R 0 is not too large. However, if R 0 is large, Wolbachia strains that reduce but do not eliminate dengue transmission have little effect on endemic steady states or epidemic sizes. Unless control measures to reduce R 0 by reducing mosquito populations are also put in place, it may be worth the extra effort in such cases to introduce Wolbachia strains that eliminate dengue transmission completely.