A promising method of concentrating X-and soft γ-rays from celestial sources is a Laue lens. A new scheme for this lens, relying on diffraction in curved Si and Ge crystals, is introduced here. The proposed Laue lens is based on high-efficiency diffraction of curved (111) or (224) crystalline planes, which are bent through quasi-mosaic effect. While diffraction in curved (111) quasi-mosaic crystals is well known and has recently been proposed for a Laue lens, diffraction by quasi-mosaic (224) planes is suggested and demonstrated here through experimental work carried out at the Institut Laue-Langevin (ILL, Grenoble, France) at DIGRA, a facility specifically built for characterizing instrumentation in Astrophysics. Results show that the diffraction efficiency in the (224) quasimosaic sample is amplified by more than one order of magnitude with respect to an equivalent crystal without quasi-mosaic effect. The lens has been designed in such a way as to maximize and smoothen its sensitivity, thanks to a custom-made code based on a genetic algorithm.