Excess mortality has been used to measure the impact of COVID-19 over time and across countries. But what baseline should be chosen? We propose two novel approaches: an alternative retrospective baseline derived from the lowest weekly death rates achieved in previous years and a within-year baseline based on the average of the 13 lowest weekly death rates within the same year. These baselines express normative levels of the lowest feasible target death rates. The excess death rates calculated from these baselines are not distorted by past mortality peaks and do not treat non-pandemic winter mortality excesses as inevitable. We obtained weekly series for 35 industrialized countries from the Human Mortality Database for 2000-2020. Observed, baseline and excess mortalities were measured by age-standardized death rates. We assessed weekly and annual excess death rates driven by the COVID-19 pandemic in 2020 and those related to seasonal respiratory infections in earlier years. There was a distinct geographic pattern with high excess death rates in Eastern Europe followed by parts of the UK, and countries of Southern and Western Europe. Some Asia-Pacific and Scandinavian countries experienced lower excess mortality. In 2020 and earlier years, the alternative retrospective and the within-year excess mortality figures were higher than estimates based on conventional metrics. While the latter were typically negative or close to zero in years without extraordinary epidemics, the alternative estimates were substantial. Cumulation of this "usual" excess over 2-3 years results in human losses comparable to those caused by COVID-19. Challenging the view that non-pandemic seasonal winter mortality is inevitable would focus attention on reducing premature mortality in many countries. As SARS-CoV-2 is unlikely to be the last respiratory pathogen with the potential to cause a pandemic, such measures would also strengthen global resilience in the face of similar threats in the future.