When treating the ground-state contribution exactly, a variant of the saddl
e-point method emerges that works even for condensed Bose gases. Results th
us obtained, such as canonical partition functions, differ by universal ren
ormalization factors from those provided by the conventional but incorrect
scheme. The amended method yields the statistical properties of ideal and v
ery weakly interacting Bose gases with a fixed number of particles with par
ticular simplicity. [S1063-651X(99)13012-5].