  We investigate the critical scaling behavior of finite systems in the
canonical ensemble. The essential difference with the grand canonical ensemble.
i.e., the constraint on the number of particles, is already known to lead to
the Fisher renormalization phenomenon that modifies the thermal critical
singularities. We show that, in observables that are not Fisher renormalized,
it also leads to a finite-size effect governed by an exponent $y_1$ that
depends on the temperature exponent $y_t$ and the dimensionality $d$ as
$y_1=-|2y_t-d|$. We verify this prediction by a Monte Carlo analysis of several
two-dimensional lattice models in the percolation, the Ising and the 3-state
Potts universality classes.
