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Tankless water heaters offer significant energy savings over conventional storage-tank water heaters, because thermal losses to the environment are much less. Although standard test results are available to compare tankless heaters with storage tank heaters, actual savings depend on the draw details because energy to heat up the internal mass depends on the time since the last draw. To allow accurate efficiency estimates under any assumed draw pattern, a one-node model with heat exchanger mass is posed here. Key model parameters were determined from test data. Burner efficiency showed inconsistency between the two data sets analyzed. Model calculations show that efficiency with a realistic draw pattern is ~8% lower than that resulting from using only large ~40 liter draws, as specified in standard water-heater tests. The model is also used to indicate that adding a small tank controlled by the tankless heater ameliorates unacceptable oscillations that tankless with feedback control can experience with pre-heated water too hot for the minimum burner setting. The added tank also eliminates problematic low-flow cut-out and hot-water delay, but it will slightly decrease efficiency. Future work includes model refinements and developing optimal protocols for parameter extraction.