Mixed-phase clouds are ubiquitous in all regions of Earth, yet are poorly constrained due to difficulty in obtaining observations of these clouds. Many models underestimate the supercooled liquid proportion of mixed-phase clouds, which biases estimates of the Earth’s radiation budget due to the contrasting optical properties of liquid droplets and ice crystals. Using global satellite observations obtained by NASA’s CALIOP instrument, mixed-phase clouds simulated by NCAR’s global climate model, CESM, are constrained by tuning various microphysical parameters relevant to mixed-phase clouds processes in its atmospheric model component, CAM5. The equilibrium climate sensitivity estimates of the satellite-constrained simulations range from 5 to 5.3 degrees Celsius, which is up to 1.3 degrees Celsius greater than the standard simulation and 2.1 degrees Celsius greater than the CMIP archive ensemble mean. The higher equilibrium climate sensitivity estimates are linked to a weakened negative cloud phase feedback that depends on the supercooled liquid proportion of its mixed-phase clouds in the initial state. Climate models that underestimate the supercooled liquid proportion in the initial state are shown to exhibit an unrealistically strongly negative cloud phase feedback that counteracts warming that would otherwise occur.