Environmental indicators based on the life cycle assessment (LCA) method are integrated into an energy system model (ESM). This integration allows for the generation of comprehensive environmental assessments of future energy systems and for determining energy scenarios with low environmental impacts and moderate cost increases. In Switzerland, which is used as a case study to demonstrate the feasibility of our approach, it is possible to generate pathways with a 5% cost increase on the cost-optimal situation, causing an impact score for climate change that is 2% higher than the minimum feasible solution. The minimization of life-cycle impacts on climate change generates substantial environmental co-benefits with regards to human health, air pollution, ozone depletion, acidification, and land transformation. However, that minimization also creates trade-offs that exacerbate the effects of metal depletion and human toxicity caused by upstream extraction and manufacturing linked to technologies such as solar panels and electric vehicles. Finally, ambitious reduction targets of 95% direct (i.e., within the country) CO2 emissions for the year 2050 might still result in substantial climate change impacts should emissions embodied in the infrastructure and upstream supply chain not be jointly mitigated jointly.