A planar steady flame is assumed to propagate through a mixture of fuel, oxidant, diluent and product species, which burns according to a general one-step reversible reaction. On the assumption that the activation energy of the burning reaction is large, the first significant terms in asymptotic series for several quantities of interest are evaluated. As a result it is possible to make some general observations about the effects of mixture strength on a number of features, such as flame propagation speed and reaction-zone behaviour, for example. It is also deduced that chemical-reaction induced amplification of acoustic disturbances is unlikely to occur in pre-mixed flames of this simple type.