Optimization models for minimizing pollutant exposure from groundwater resources require time and resources that many communities might not have ready access to due to their economic conditions. In such cases, it might be useful to develop a “rule of thumb” approach for suggestions in case of uncertainties and inadequate means to address these uncertainties. Monte Carlo analysis was performed for a simplified groundwater system and the effects of extraction patterns, distance to pollution source, dispersivity, pollutant pulse period, pore water velocity and decay were examined for minimizing the high pollutant exposure risk from the extracted groundwater. Results indicate that, in a high uncertainty scenario, the best bet for minimizing the risk of high pollutant exposure would be to adopt a frequent extraction pattern and supply the water as a mixture of extractions from multiple wells spread over an area. These findings can be used as a “rule of thumb” wherever time and resources might be the limiting factors.