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Recent Arctic sea ice retreat has been quicker than in most general circulation model (GCM) simulations. Internal variability may have amplified the observed retreat in recent years, but reliable attribution and projection requires accurate representation of relevant physics. Most current GCMs do not fully represent falling ice radiative effects (FIREs), and here we show that the small set of Coupled Model Intercomparison Project Phase 5 (CMIP5) models that include FIREs tend to show faster observed retreat. We investigate this using controlled simulations with the CESM1-CAM5 model. Under 1pctCO2 simulations, including FIREs results in the first occurrence of an "ice-free" Arctic (monthly mean extent < 1 x 10(6) km(2)) at 550 ppm CO2, compared with 680 ppm otherwise. Over 60-90 degrees N oceans, snowflakes reduce downward surface shortwave radiation and increase downward surface longwave radiation, improving agreement with the satellite-based CERES EBAF-Surface dataset. We propose that snowflakes' equivalent greenhouse effect reduces the mean sea ice thickness, resulting in a thinner pack whose retreat is more easily triggered by global warming. This is supported by the CESM1-CAM5 surface fluxes and a reduced initial thickness in perennial sea ice regions by approximately 0.3 m when FIREs are included. This explanation does not apply across the CMIP5 ensemble in which inter-model variation in the simulation of other processes likely dominates. Regardless, we show that FIRE can substantially change Arctic sea ice projections and propose that better including falling ice radiative effects in models is a high priority.