  We present an efficient method of calculating exact confidence intervals for
the hypergeometric parameter representing the number of "successes," or
"special items," in the population. The method inverts minimum-width acceptance
intervals after shifting them to make their endpoints nondecreasing while
preserving their level. The resulting set of confidence intervals achieves
minimum possible average size, and even in comparison with confidence sets not
required to be intervals it attains the minimum possible cardinality most of
the time, and always within $1$. The method compares favorably with existing
methods not only in the size of the intervals but also in the time required to
compute them. The available \textsf{R} package \texttt{hyperMCI} implements the
proposed method.
