  The interplay between between gauge-field winding numbers, theta-vacua, and
the Dirac operator spectrum in finite-volume gauge theories is reconsidered. To
assess the weight of each topological sector, we compare the mass-dependent
chiral condensate in gauge field sectors of fixed topological index with the
answer obtained by summing over the topological charge. Also the microscopic
Dirac operator spectrum in the full finite-volume Yang-Mills theory is obtained
in this way, by summing over all topological sectors with the appropriate
weight.
