Clessidra (hour-glass) X-ray lenses have an overall shape of an old hour glass, in which two opposing larger triangular prisms are formed of smaller identical prisms or prism-like objects. In these lenses, absorbing and otherwise optically inactive material was removed with a material-removal strategy similar to that used by Fresnel in the lighthouse lens construction. It is verified that when the single prism rows are incoherently illuminated they can be operated as independent micro-lenses with coinciding image positions for efficient X-ray beam concentration. Experimental data for the line width and the refraction efficiency in one-dimensional focusing are consistent with the expectations. Imperfections in the structures produced by state-of-the-art deep X-ray lithography directed only 35% of the incident intensity away from the image and widened it by just 10% to 125 microm. An array of micro-lenses with easily feasible prism sizes is proposed as an efficient retrofit for the refocusing optics in an existing beamline, where it would provide seven-fold flux enhancement.