The present disclosure is directed to the operation and turndown of a segmented annular combustion system. The method includes injecting, via a fuel nozzle, a combustible mixture into a primary combustion zone between an adjacent pair of integrated combustor nozzles and burning the combustible mixture. The method further includes flowing air and injecting fuel into a premixing channel defined within a first integrated combustor nozzle to produce a second combustible mixture. The second combustible mixture is injected into a secondary combustion zone where it is combusted. The flow of combustion gases is accelerated, via turbine nozzles of the integrated combustor nozzles, toward turbine blades of a downstream turbine section. The method permits turndown of the combustion system by reducing or shutting off fuel to various components of the combustion system.