The strong reduction of air traffic during the COVID-19 pandemic provides a unique test case for the relationship between air traffic density, contrails, and their radiative forcing of climate change. Here, air traffic and contrail cirrus changes are quantified for a European domain for March to August 2020 and compared to the same period in 2019. Traffic data show a 72 % reduction in flight distance compared with 2019. This paper investigates the induced contrail changes in a model study. The contrail model results depend on various methodological details as discussed in parameter studies. In the reference case, the reduced traffic caused a reduction in contrail length. The reduction is slightly stronger than expected from the traffic change because the weather conditions in 2020 were less favorable for contrail formation than in 2019. Contrail coverage over Europe with an optical depth larger than 0.1 decreased from 4.6 % in 2019 to 1.4 % in 2020; the total cirrus cover amount changed by 28 % to 25 %. The reduced contrail coverage caused 70 % less longwave and 73 % less shortwave radiative forcing but, because of various nonlinearities, only 54 % less net forcing in this case. The methods include recently developed models for performance parameters and soot emissions. The overall propulsion efficiency of the aircraft is about 20 % smaller than estimated in earlier studies, resulting in 3 % fewer contrails. Considerable sensitivity to soot emissions is found, highlighting fuel and engine importance. The contrail model includes a new approximate method to account for water vapor exchange between contrails and background air and for radiative forcing changes due to contrail–contrail overlap. The water vapor exchange reduces available ice supersaturation in the atmosphere, which is critical for contrail formation. Contrail–contrail overlap changes the computed radiative forcing considerably. Comparisons to satellite observations are described and discussed in a parallel publication.