Variational estimates of the effect of flux shifts on the integral reactivity parameter of the point-kinetics equations and on regional power fractions were calculated for a variety of localized perturbations in two light water reactor (LWR) model problems representing a small, tightly coupled core and a large, loosely coupled core. For the small core, the flux shifts resulting from even relatively large localized reactivity changes (∼600 pcm) were small, and the standard point-kinetics approximation estimates of reactivity were in error by only ∼10% or less, while the variational estimates were accurate to within ∼1%. For the larger core, significant (>50%) flux shifts occurred in response to local perturbations, leading to errors of the same magnitude in the standard point-kinetics approximation of the reactivity worth. For positive reactivity, the error in the variational estimate of reactivity was only a few percent in the larger core, and the resulting transient power prediction was 1 to 2 orders of magnitude more accurate than with the standard point-kinetics approximation. For a large, local negative reactivity insertion resulting in a large flux shift, the accuracy of the variational estimate broke down. The variational estimate of the effect of flux shifts on reactivity in point-kinetics calculations of transients in LWR cores was found to generally result in greatly improved accuracy, relative to the standard point-kinetics approximation, the exception being for large negative reactivity insertions with large flux shifts in large, loosely coupled cores.