Combining the advantages of photon sieves (PSs) and compound Fresnel zone plates (CZPs), we designed compound photon sieves (CPSs) for hard-x-ray nanofocusing. A CPS consists of an inner PS using the first-order diffraction surrounded by an outer zone plate using the third-order diffraction. A robust digital prolate spheroidal window was used as an apodization window for the inner PS, making CPSs more flexible than CZPs. CPSs can provide not only slightly better resolution compared to CZPs, but also it can significantly suppress the sidelobes, leading to a high signal-to-noise ratio. Further improvement of the high-aspect-ratio metal nanostructure process will allow CPSs to be a promising candidate for hard-x-ray nanofocusing in the high-energy region above 20 keV.