Although the vaccine against measles has been routinely applied over a quarter of a century, measles is still an active disease in Israel. The January 1991 outbreak caused high morbidity in infant and adolescent populations and high mortality, especially among nomad Bedouins in the southern region of the country. The Bedouins form a small fraction of the total Israeli population (ca. 2%), but it is thought that they may experience significantly higher rates of transmission than the majority group. In this work we use deterministic compartmental mathematical models to define the optimal immunization strategy for a population consisting of a majority group characterized by low transmission rates and a minority group characterized by high transmission rates; this study allows both for transmission differences between the two groups, and for possible differences in the average cost (or difficulty) in reaching individuals for vaccination. Our analysis shows that the optimal vaccination policy for such a population involves different strategies for the two groups: a smaller fraction is to be vaccinated in the minority group if transmission in this group is not much larger than in the majority group, whereas, if the difference in transmission is very large, a higher proportion is to be vaccinated in the minority group. The advantage of this non-uniform vaccination policy is that it involves vaccination of a smaller fraction of the total population (and costs less, if there are differential costs between the groups), as compared with the proportion vaccinated under the conventional uniform vaccination policy. The implications of our results for vaccination policies for other minority groups, or for other infectious diseases which are characterized by epidemiological heterogeneity, are as yet to be examined.