The spatial scan statistic is a widely applied tool for cluster detection. The spatial scan statistic evaluates the significance of a series of potential circular clusters using Monte Carlo simulation to account for the multiplicity of comparisons. In most settings, the extent of the multiplicity problem varies across the study region. For example, urban areas typically have many overlapping clusters, while rural areas have few. The spatial scan statistic does not account for these local variations in the multiplicity problem. We propose two new spatially-varying multiplicity adjustments for spatial cluster detection, one based on a nested Bonferroni adjustment and one based on local averaging. Geographic variations in power for the spatial scan statistic and the two new statistics are explored through simulation studies, and the methods are applied to both the well-known New York leukemia data and data from a case-control study of breast cancer in Wisconsin.