I will present a new algorithm to calculate exact hypervolumes. Given
a set of $d$-dimensional points, it computes the
hypervolume of the dominated space. Determining this value is an
important subroutine of Multiobjective Evolutionary Algorithms
(MOEAs). We analyze the ``Quick Hypervolume'' QHV algorithm
theoretically and experimentally. The theoretical results are
a significant contribution to the current state of the art. Moreover
the experimental performance is also very competitive, compared
with existing exact hypervolume algorithms.