A successful fight against COVID-19 greatly depends on citizens' adherence to the restrictive measures, which may not suffice alone. Making use of a containment index, data on sanctions, and Google's movement trends across Italian regions, complemented by other sources, we investigate the extent to which compliance with the mobility limitations has affected the number of deaths over time in the period from the 24th of February 2020 to the 9th of November 2020, by using panel data for Italian regions, analysed through a negative binomial regression method. We also differentiated the study period, estimating two distinct models on two subsamples: until the 13th of September and since the 14th of September. In so doing, we show how the pandemic dynamics have changed between the first and the second wave of the emergency. Our results highlight that the importance of the restrictive measures and of citizens' accord on their abidance has greatly increased since the end of the summer, also because the stringency level of the adopted measures has critically declined. Informing citizens about the effects and purposes of the restrictive measures is of paramount importance, especially in the current phase of the pandemic.