Measles eradication efforts have been successful at achieving elimination in many countries worldwide. Such countries actively work to maintain this elimination by continuing to improve coverage of two routine doses of measles vaccine following measles elimination. While improving measles vaccine coverage is always beneficial, we show, using a steady-state analysis of a dynamical model, that the correlation between populations receiving the first and second routine dose also has a significant impact on the population immunity achieved by a specified combination of first and second dose coverage. If the second dose is administered to people independently of whether they had the first dose, high second-dose coverage improves the proportion of the population receiving at least one dose, and will have a large effect on population immunity. If the second dose is administered only to people who have had the first dose, high second-dose coverage reduces the rate of primary vaccine failure, but does not reach people who missed the first dose; this will therefore have a relatively small effect on population immunity. When doses are administered dependently, and assuming the first dose has higher coverage, increasing the coverage of the first dose has a larger impact on population immunity than does increasing the coverage of the second. Correlation between vaccine doses has a significant impact on the level of population immunity maintained by current vaccination coverage, potentially outweighing the effects of age structure and, in some cases, recent improvements in vaccine coverage. It is therefore important to understand the correlation between vaccine doses as such correlation may have a large impact on the effectiveness of measles vaccination strategies.