Current microscopy demands the visualization of large threedimensional samples with increased sensitivity, higher resolution, and faster speed. Several imaging techniques based on widefield, point-scanning, and light-sheet strategies have been designed to tackle some of these demands. Although successful, all these require the illuminated volumes to be tightly coupled with the detection optics to accomplish efficient optical sectioning. Here, we break this paradigm and produce optical sections from out-of-focus planes. This is done by extending the depth of field of the detection optics in a lightsheet microscope using wavefront-coding techniques. This passive technique allows accommodation of the light sheet at any place within the extended axial range. We show that this enables quick scanning of the light sheet across a volumetric sample. As a consequence, imaging speeds faster than twice the volumetric video rate (>70 volumes/s) can be achieved without needing to move the sample. These capabilities are demonstrated for volumetric imaging of fast dynamics in vivo as well as for fast, three-dimensional particle tracking.