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Background: The novel coronavirus disease is an ongoing pandemic that started in China in December 2019. This paper is aimed at estimating the first two infections waves in Italy in relation to adopted health policies. Design and methods: We moved deaths of the Italian COVID-19 registry from recorded to infection date by the weighted moving average. We considered two infection fatality ratios related to the effective or saturated health system, we estimated the likely incidence curve from the resulting deaths and evaluated the curve shape before and after the national health policies. Results: From the 24th of February 2020 to the 7th of February 2021, we estimated 6,664,655 (4,639,221-9,325,138) cases distributed on two waves. Suitable daily infection fatality rates were 2.53% within the first wave and 1.15% within the second one. The first wave (February-July 2020) had its peak on the 14th of March 2020 (26,575). The second wave (August 2020-February 2021) was fatter with the peak on the 12th of November (60,425) and a hump in December before decreasing to 26,288 at the end. Adopted health policies were followed by changes in the curve rate. Conclusions: Tracing infection contacts and quarantining asymptomatic people reduced virus lethality in the second wave. Restriction on population mobility is effective within a suppression strategy, distance learning reduces contacts among families. Removal of restrictions should be implemented by sequential steps for avoiding a quick rising of incident cases. A reasonable public health daily goal to control both virus spread and lethality could be to find at least 87 cases for each death. [ABSTRACT FROM AUTHOR]