Abstract Full pump depletion corresponds to the upper limit of the generated signal photons relative to the pump pulse; this allows the highest peak power to be produced in a unit area of ultraintense laser amplifiers. In practical systems based on optical parametric chirped-pulse amplification, however, the typical pump depletion is only ~35%. Here, we report quasi-parametric chirped-pulse amplification (QPCPA) with a specially designed 8-cm-thick Sm:YCOB crystal that highly dissipates the idler and hence improves pump depletion. We demonstrate 56% QPCPA energy efficiency for an 810-nm signal converted from a 532-nm pump, or equivalently 85% pump depletion. As another advantage, such a record high depletion greatly suppresses the parametric superfluorescence noise in QPCPA to only ~1.5 × 10 −6 relative to the amplified signal energy. These results pave the way to beyond the ten-petawatt peak power of the currently most intense lasers.