We report on a versatile method to compensate the linear attenuation in a medium, independently of its microscopic origin. The method exploits diffraction-limited Bessel beams and tailored on-axis intensity profiles, which are generated using a phase-only spatial light modulator. This technique for compensating one of the most fundamental limiting processes in linear optics is shown to be efficient for a wide range of experimental conditions (modifying the refractive index and the attenuation coefficient). Finally, we explain how this method can be advantageously exploited in applications ranging from bio-imaging light sheet microscopy to quantum memories for future quantum communication networks.