One of main challenges in light-sheet microscopy is to design the light-sheet as extended and thin as possible--extended to cover a large field of view, thin to optimize resolution and contrast. However, a decrease of the beam's waist also decreases the illumination beam's depth of field. Here, we introduce a new kind of beam that we call sectioned Bessel beam. These beams can be generated by blocking opposite sections of the beam's angular spectrum. In combination with confocal-line detection the optical sectioning performance of the light-sheet can be decoupled from the depth of field of the illumination beam. By simulations and experiments we demonstrate that these beams exhibit self-reconstruction capabilities and penetration depths into thick scattering media equal to those of conventional Bessel beams. We applied sectioned Bessel beams to illuminate tumor multicellular spheroids and prove the increase in contrast. Sectioned Bessel beams turn out to be highly advantageous for the investigation of large strongly scattering samples in a light-sheet microscope.