Today's gas tankless water heaters offer significant energy savings over conventional gas storage tank water heaters, but savings depends on the draw pattern. A one-node model incorporating heat exchanger mass is used to address this and other issues. Key model parameters are determined from least-squares regression on short-term data, including burner efficiency, thermal capacitance, and thermal loss coefficient. The calibrated model agrees with data to approximately 5% on Qgas, with temperature RMS deviation of approximately 4 degrees C. Efficiency with a standard realistic draw is 71%, compared to 81% predicted from standard energy-factors. Adding a small tank controlled by the tankless heater solves issues of oscillations with solar pre-heat, low-flow and hot-water-delay issues. Future work includes model refinements and developing optimal data protocols for model parameter extraction.