With a dataset from all 20 Finnish regions spanning a time period from 1950 to 2010, this article analyses how the market share mobility index in newspaper circulation and ownership has developed over time and whether entry and exit have played any significant role therein. It compares the results obtained at the ownership level with those of the newspaper level and infers whether the market share mobility index complements or substitutes the conventional concentration measures. The results show that entry and exit of newspapers have not contributed significantly to the market share mobility index and that analysis of ownership and newspaper circulation yields remarkably different results. Our conjecture that market share mobility would peak in the decade of a severe economic downturn was not indisputably upheld. The results indicate that traditional concentration measures and compound market indices should rather be seen as allies than rivals.