[bibtex key=ApterCummingsHamkins2006:LargeCardinalsWithFewMeasures]

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