Desulfation methods for an exhaust treatment system having a fuel reformer configured upstream of a LNT. Reductant is injected upstream of the fuel reformer. The reductant reacts within the reformer to generate heat, but the system is configured for some reductant to breakthrough and react in the LNT to generate further heat. This configuration allows the LNT to operate at temperatures higher the than first device and facilitates independent control of the LNT and first device temperatures. An outer loop controls the LNT temperature by issuing instructions to an inner loop that controls the reformer. Typically, the inner loop will pulse the reductant injection rate in order to limit the reformer temperature. The outer loop can pulses the loop on a longer time scale, resulting in two pulse periods. Through timing, a reformate peak from one period is made to overlap a temperature peak from a previous period.