Efficient cladding-pumped three-level Yb fiber lasers are difficult to achieve due to the competing four-level system and necessary high inversions. We demonstrate an efficiency of ∼62.7% versus a coupled pump, a record for cladding-pumped fiber lasers with a single-pass pump. 84 W at ∼978 nm with ∼1.12M2 was achieved, a record power for flexible fibers. Amplified spontaneous emission was suppressed by >40 dB. The efficiency is quantum-limited ∼94% versus an absorbed pump. This is made possible by the use of a photo-darkening-free Yb phosphosilicate core and recent progress in single-mode large-core all-solid photonic bandgap fiber designs, which provide the necessary large core-to-cladding ratio and suppression of the four-level system.