X-ray nanofocusing devices are capable of focusing X-rays down to sizes of about 10 nm. We have developed a new nanofocusing device, known as total-reflection zone plates (TRZPs), for focusing high-brilliance synchrotron radiation in the hard x-ray region. This device consists of a reflective zone pattern on a flat substrate. It has the potential to focus hard x-rays down to sub-10-nm dimensions. Furthermore, it is considerably easier to fabricate than other hard x-ray nanofocusing devices since it is used with a very small grazing incidence angle. We have focused 10-keV x-rays to sub-15 nm dimensions using a TRZP that was fabricated by conventional electron-beam lithography. In addition, we present designs for more efficient devices that have a target focus size of 5 nm. We propose and discuss a new approach for achieving point focusing with nanometer dimensions.