The standard method for p-value computation of spatial scan statistics, with adjustments for covariate effects, is to conduct Monte Carlo simulations with these effects estimated under the null hypothesis of no clustering. However when the covariates are geographically unbalanced, the proposed Monte Carlo p-value estimates are too conservative, with corresponding loss of power, due to excessive adjustments for confounding between covariates and location. We show that the use of an alternative procedure that involves local score statistics, with parameters fitted on a log-linear or logistic model, addresses this problem. We also discuss extensions of the procedure when there are multiple or continuous covariates. Copyright © 2010 John Wiley & Sons, Ltd.