A critique is presented of the frequently used Bruce-Wilding (BW) mixed-field scaling method for estimating the critical points of nonsymmetric model fluids from grand canonical simulation data. An explicit, systematic technique for implementing this method is set out, thereby revealing clearly a fortunate, close cancelation of contributions from the leading correction-to-scaling and thermal scaling functions that makes the method effective for Ising-type systems but that lacks a general theoretical basis. The BW approach does not allow for pressure mixing in the scaling fields, which is essential for representing a Yang-Yang anomaly (namely, the divergence at criticality of the second temperature derivative, (d(2)mu(sigma)/dT(2)), of the chemical potential mu(sigma)(T) on the phase boundary), but such behavior must be expected in realistic models. We show that allowance for pressure mixing does not alter the leading dependence of the critical temperature estimator, T-c(L), on the linear size, L, of the simulation box: this converges as L-(1+theta)/nu when L --> infinity (where nu similar or equal to 0.6 and theta similar or equal to 0.5 are the correlation length and leading correction critical exponents). On the other hand, the critical density estimator, rho(c)(L), gains a leading variation proportional toL(-2beta/nu) that dominates the previously claimed L-(1-alpha)/nu term (where alpha similar or equal to 0. 1 and beta similar or equal to 0.3 are the specific heat and coexistence curve exponents). Numerically, the BW method provides estimates of T-c consistent with those obtained from recently developed unbiased techniques that do not require prior knowledge of the universal order-parameter and energy distribution functions; however, BW estimates of the critical densities, rho(c), prove significantly less reliable.