This article considers two coarse measures applicable to antitrust policy: one of market concentration, the Herfindahl-Hirschman Index (HHI) and one of market dominance, threshold value. Calculations of threshold value are compared to HHI values to determine when thresholds might be of specific use in merger cases. Many scenarios which satisfy the threshold conditions (indicating a dominant firm exists) are consistent with high HHI numbers such that current US Department of Justice and European Commission guidelines (based on HHIs) for merger concerns will have been met. It is suggested as a rule of thumb that HHIs be used as necessary conditions and threshold value be considered sufficient conditions for further case review.