Tankless water heaters do not conserve water. They conserve energy only, by using less natural gas to heat water.
The best way to conserve water with a regular tank water heater is to install a hot water pump attached to the hot water supply of the water heater along with a special valve installed under the kitchen sink and the bathroom sink.
We have this device on our water heater and, before it was installed, it took 5 gallons of water to run before it got hot at the spigot in the kitchen.
With the pump installed, it is almost instantly hot, therefore saving a lot of water.
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It also helps with the washing machine and dishwasher, as well as in the showers. A tankless water heater does not get hot water to a spigot any faster. It only saves on energy use, which is a good thing if there is no drought situation.
The only major drawback to installing the pump is that it requires a 12-volt power supply to operate the pump.