High-efficiency optical storage in rare-earth-ion-doped crystals is challenging because of their typically weak optical absorption,which makes cavity-enhanced memories highly sensitive to parasitic intracavity loss. Here we demonstrate a 90.1(5)% storage efficiency for coherent optical pulses in an impedance-matched cavity atomic-frequency-comb memory based on Eu3+:Y2SiO5. The Brewster-angle configuration of the crystal and fully cryogenic Fabry-Pérot cavity reduce the round-trip intracavity loss to 0.37%. Quantitative modeling shows that further improvement is limited primarily by AFC preparation and its associated dispersive response rather than by residual cavity loss,identifying the principal requirements for further approaching unity efficiency.