[bibtex key=ApterCummingsHamkins2006:LargeCardinalsWithFewMeasures]

We show, assuming the consistency of one measurable cardinal, that it is consistent for there to be exactly 𝜅+ many normal measures on the least measurable cardinal 𝜅. This answers a question of Stewart Baldwin. The methods generalize to higher cardinals, showing that the number of 𝜆-strong compactness or 𝜆-supercompactness measures on 𝑃𝜅⁡(𝜆) can be exactly 𝜆+, if 𝜆 >𝜅 is a regular cardinal. We conclude with a list of open questions. Our proofs use a critical observation due to James Cummings.