We construct a new class of physical states of the free Klein-Gordon field in Robertson-Walker spacetimes. This is done by minimizing the expectation value of smeared stress-energy. We get an explicit expression for the state depending on the smearing function. We call it a state of low energy. States of low energy are an improvement of the concept of adiabatic vacua on Robertson-Walker spacetimes. The latter are approximations of the former. It is shown that states of low energy are Hadamard states.