There are observations that right after total quarantine measures were introduced, there was no growth in number of suicides, but a situation remains unclear when it comes down to new waves in the pandemic development. Our research goal was to estimate risks of suicide in heterogeneous population groups in 2020, that is, from the pandemic start and up to the second wave rise. We analyzed data on completed suicides in Saint Petersburg, Udmurtia Republic (Russia), and Odessa region (Ukraine), 6375 cases overall among population groups with total number of people being equal to 9,216 thousand starting from January 01, 2016 to December 31, 2020. Confidence intervals for frequencies as per months (per 100,000 people) in 2020 were calculated as per Wilson and compared with average ones calculated for 2016–2019. There was a decrease in frequency of completed suicides in all three population groups during a period when the strictest quarantine measures were valid; by the mid-summer the trend normalized or there was even a slight increase. When the second pandemic wave came, changes were multidirectional; in particular, in Saint Petersburg there was another decrease by the end of the year, the most apparent and statistically significant among men whereas there were short-term rises in Udmurtia and Odessa. Our comparison performed for population groups with initially different levels of suicides confirms that right after a crisis starts, suicidal behavior becomes less frequent among people; however, as a response to the second pandemic wave, we can expect both falls and rises in number of suicides and it requires more intense preventive activities.