Mathematical models have recently been used to predict the future burden of multidrug-resistant tuberculosis (MDRTB). These models suggest the threat of multidrug resistance to TB control will depend on the relative 'fitness' of MDR strains and imply that if the average fitness of MDR strains is considerably less than that of drug-sensitive strains, the emergence of resistance will not jeopardize the success of tuberculosis control efforts. Multidrug resistance in M. tuberculosis is conferred by the sequential acquisition of a number of different single-locus mutations that have been shown to have heterogeneous phenotypic effects. Here we model the impact of initial fitness estimates on the emergence of MDRTB assuming that the relative fitness of MDR strains is heterogeneous. We find that even when the average relative fitness of MDR strains is low and a well-functioning control program is in place, a small subpopulation of a relatively fit MDR strain may eventually outcompete both the drug-sensitive strains and the less fit MDR strains. These results imply that current epidemiological measures and short-term trends in the burden of MDRTB do not provide evidence that MDRTB strains can be contained in the absence of specific efforts to limit transmission from those with MDR disease.