The fundamental differences between the leading-order jump conditions, often assumed at a flame sheet in combustion theory, and the actual effect of a chemical reaction that satisfies Arrhenius kinetics with a finite activation temperature, need to be understood. These differences are "higher order" in terms of a large activation temperature analysis. However, they do provide a quantitative estimate of the errors that are inherent in adopting only the leading order version and they can indicate qualitative changes that may occur at finite activation temperatures in some cases. This paper derives two orders of asymptotic correction to the jump conditions normally used in describing premixed laminar combustion. An example involving steady, non-adiabatic flame-balls shows that the accepted asymptotic picture is limited to unusually large Zel'dovich numbers.