The aim of this paper is to showcase different decarbonization pathways for Europe with varying Carbon dioxide (CO2) constraints until 2050. The Global Energy System Model (GENeSYS-MOD) framework, a linear mathematical optimization model, is used to compute low-carbon scenarios for 17 European countries or regions. The sectors power, low- and high- temperature heating, and passenger and freight transportation are included, with the model endogenously constructing capacities in each period. Emission constraints differ between different scenarios and are either optimized endogenously by the model, or distributed on a per-capita basis, GDP-dependent, or based on current emissions. The results show a rapid phase-in of renewable energies, if a carbon budget in line with established international climate targets is chosen. It can be shown that the achievement of the 2° target can be met with low additional costs compared to the business as usual case, while reducing total emissions by more than 30%.