Global climate model (GCM) estimates of the equilibrium global mean surface temperature response to a doubling of atmospheric CO2, measured by the equilibrium climate sensitivity (ECS), range from 2.0° to 4.6°C. Clouds are among the leading causes of this uncertainty. Here we show that the ECS can be up to 1.3°C higher in simulations where mixed-phase clouds consisting of ice crystals and supercooled liquid droplets are constrained by global satellite observations.The higher ECS estimates are directly linked to a weakened cloud-phase feedback arising from a decreased cloud glaciation rate in a warmer climate.We point out the need for realistic representations of the supercooled liquid fraction in mixed-phase clouds in GCMs, given the sensitivity of the ECS to the cloud-phase feedback.