Several kinds of sampling methods (simple random sampling, regular grids, preferential grids, stratified random sampling, and importance sampling) and estimators (polygons of influence and kriging) were used with simulated data to estimate the average level of a pollutant that is highly concentrated around a source. Very precise estimates were given by stratified sampling with a regular grid in each stratum, the grid spacing being reduced in the stratum with the highest concentration. Stratified random sampling and importance sampling gave more variable estimates, but allowed the sampling variance to be estimated from a single sample. Estimates from polygons of influence and kriging were biased, and the kriging variances often differed greatly from the observed sampling variance of the kriging estimates.