Scattering and absorption limit the penetration of optical fields into tissue. We demonstrate a new approach for increased depth penetration in light-sheet microscopy: attenuation-compensation of the light field. This tailors an exponential intensity increase along the illuminating propagation-invariant field, enabling the redistribution of intensity strategically within a sample to maximize signal and minimize irradiation. A key attribute of this method is that only minimal knowledge of the specimen transmission properties is required. We numerically quantify the imaging capabilities of attenuation-compensated Airy and Bessel light sheets, showing that increased depth penetration is gained without compromising any other beam attributes. This powerful yet straightforward concept, combined with the self-healing properties of the propagation-invariant field, improves the contrast-to-noise ratio of light-sheet microscopy up to eightfold across the entire field of view in thick biological specimens. This improvement can significantly increase the imaging capabilities of light-sheet microscopy techniques using Airy, Bessel, and other propagation-invariant beam types, paving the way for widespread uptake by the biomedical community.