  We study the bond percolation problem under the constraint that the total
number of occupied bonds is fixed, so that the canonical ensemble applies. We
show via an analytical approach that at criticality, the constraint can induce
new finite-size corrections with exponent y_{can}=2y_t-d both in energy-like
and magnetic quantities, where y_t=1/{\nu} is the thermal renormalization
exponent and d is the spatial dimension. Furthermore, we find that while most
of universal parameters remain unchanged, some universal amplitudes, like the
excess cluster number, can be modified and become non-universal. We confirm
these predictions by extensive Monte Carlo simulations of the two-dimensional
percolation problem which has y_{can}=-1/2.
