Objectives: To examine (1) how a rapid data collection using a convenience sample fares in estimating change in alcohol consumption when compared to more conventional data sources, and (2) how alcohol consumption changed in Finland and Norway during the first months of the COVID-19 pandemic. Methods: Three different types of data sources were used for the 2nd quarter of 2020 and 2019: sales statistics combined with data on unrecorded consumption; the rapid European Alcohol Use and COVID-19 (ESAC) survey (Finland: n = 3800, Norway: n = 17,092); and conventional population surveys (Finland: n = 2345, Norway: n1 = 1328, n2 = 2189, n3 = 25,708). Survey measures of change were retrospective self-reports. Results: The statistics indicate that alcohol consumption decreased in Finland by 9%, while little change was observed in Norway. In all surveys, reporting a decrease in alcohol use was more common than reporting an increase (ratios 2–2.6 in Finland, 1.3–2 in Norway). Compared to conventional surveys, in the ESAC survey fewer respondents reported no change and past-year alcohol consumption was higher. Conclusion: The rapid survey using convenience sampling gave similar results on change in drinking as conventional surveys but higher past-year drinking, suggesting self-selection effects. Aspects of the pandemic driving alcohol consumption down were equally strong or stronger than those driving it up.