[en] A single-cavity buncher has been developed that resonates at both the fundamental and twice the fundamental frequency to form a more nearly ideal bunching voltage waveform in the gap. The cavity utilizes the TM₀₂₀-like mode as the first harmonic of the fundamental TM₀₁₀-like mode. Field distributions on or near the axis, which are seen by the beam, are essentially identical for the two modes. Many beam bunching applications require two bunchers with the harmonic buncher being physically as close as possible to the fundamental frequency buncher - the buncher described here accomplishes this property with a single cavity and excitation of two modes. Calculated parameters for cavity designs with a fundamental frequency of 0.45 GHz are presented for different cavity lengths which represent a range of interest for accelerators and rf tubes. Means of tuning and fabrication are described. A goemetry chosen for PIGMI is described in more detail