Global estimates of the number of domestic cats (Felis catus) are >400 million. Issues associated with free-roaming cats are of global importance because of animal-welfare and public-health concerns and impacts on native wildlife through predation, competition and disease transmission. In the United States, proposed control solutions for managing urban free-roaming cat populations include euthanasia and trap–neuter–return (TNR) programs. We evaluated control methods using a demographic population model for a 25-year period, with parameters estimated from an unmanaged, free-roaming cat population in Texas. We modelled euthanasia and TNR at 25%, 50% and 75% implementation rates and a 50 : 50 combination of euthanasia and TNR at 25%, 50%, 75% and 100% implementation rates for 0%, 25% and 50% maximum immigration rates. We compared final population size, total number of cats treated and treatment effort relative to population reduction. Population decreases were comparable among euthanasia, TNR and a 50 : 50 combination for all treatment rates when the immigration rate was 0%; however, they were higher for euthanasia at 25% and 50% maximum immigration rates. Euthanasia required higher treatment effort than TNR. Our results indicate that immigration must be prevented and high (>50%) treatment rates implemented to reduce free-roaming cat populations.