A popular mouse model of COVID-19, the K18-hACE2 mouse, expresses the SARS-coronavirus entry receptor, human angiotensin-converting enzyme 2 (hACE2) driven by the keratin-18 promoter. SARS-CoV-2-infected K18-hACE2 mice exhibit neuropathology not representative of human infection. They contain eight transgene (Tg) copies, leading to excess hACE2 expression and rampant viral replication. We generated two new lines of K18-hACE2 mice encoding one and two copies of hACE2 (1-hACE2-Tg and 2-hACE2-Tg, respectively). Relative to the original strain (called 8-hACE2-Tg in this study), 2-hACE2-Tg mice exhibited lower mortality, with less viral replication in the lung and brain. Furthermore, 1-hACE2-Tg mice exhibited no mortality and had no detectable virus in the brain; yet, they exhibited clear viral replication in the lung. All three strains showed SARS-CoV-2-related weight loss commensurate with the mortality rates. 1-hACE2-Tg mice mounted detectable primary and memory T effector cell and Ab responses. We conclude that these strains provide improved models to study hACE2-mediated viral infections.