Odd-order diffraction of zone plates (ZPs) is already used for x-ray microscopy but the potential offered by even-order diffraction must still be fully exploited. Width differences between lines and interline spaces transfer intensity from odd-order to even-order diffractions. Here we show that the resulting intense second-order diffraction provides a reasonable tradeoff between spatial resolution and intensity-and constitutes a viable strategy for x-ray microscopy to reach sub-20 nm resolution, in spite of the imperfections of high-aspect-ratio ZPs and of other difficulties.