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Small collection-electrode monolithic CMOS sensors profit from a high signal-to-noise ratio and a small power consumption, but have a limited active sensor volume due to the fabrication process based on thin high-resistivity epitaxial layers. In this paper, the active sensor depth is investigated in the monolithic small collection-electrode technology demonstrator CLICTD. Charged particle beams are used to study the charge-collection properties and the performance of devices with different thicknesses both for perpendicular and inclined particle incidence. In CMOS sensors with a high-resistivity Czochralski substrate, the depth of the sensitive volume is found to increase by a factor two in comparison with standard epitaxial material and leads to significant improvements in the hit-detection efficiency and the spatial and time resolution.