Abstract: We have conducted an investigation of the optimal embedding impedance for a waveguide superconducting hot-electron bolometric (HEB) mixer. Three mixer chip designs for 800 GHz, offering nominal embedding resistances of 70 /spl Omega/, 35 /spl Omega/, and 15 /spl Omega/, have been developed. We used both High Frequency Structure Simulator (HFSS) software and scale model impedance measurements in the design process. We subsequently fabricated HEB mixers to these designs using 3-4 nm thick NbN thin film. Receiver noise temperature measurements and Fourier Transform Spectrometer (FTS) scans were performed to determine the optimal combination of embedding impedance and normal-state resistance for a 50 Ohm IF load impedance. A receiver noise temperature of 440 K was measured at a local oscillator frequency 850 GHz for a mixer with normal state resistance of 62 /spl Omega/ incorporated into a circuit offering a nominal embedding impedance of 70 /spl Omega/. We conclude from our data that, for low noise operation, the normal state resistance of the HEB mixer element should be close to the embedding impedance of the mixer mount.