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The effects of different COVID-19 swab testing policies in Italy need investigation. We examined the relationship between the number of COVID-19 swab tests (per 10,000 population) performed from February 24 through March 27 and 7-day lagged COVID-19 mortality (per 10,000 population) in four regions of northern Italy. Lombardy, Piedmont, and initially, also Emilia-Romagna, which followed recommendations for limiting swab testing to symptomatic subjects requiring hospitalization, had a much steeper increase in mortality with increasing number of tests performed than Veneto, which applied a policy of broader testing. The relationship between tests performed and mortality declined in Emilia-Romagna in coincidence with a substantial increase in the number of tests performed on March 18. When the cumulative number of tests performed was regressed linearly toward lagged mortality in Lombardy and Veneto, the slope of the regression was 133 in Veneto and 10.4 tests per one death in Lombardy. These findings suggest that the strategy adopted in Veneto, similar to that in South Korea, was effective in containing COVID-19 epidemics and should be applied in other regions of Italy and countries in Europe.