An improved combustion system having a reduced combustion residence time in a combustion turbine engine is provided. The combustor system may include a flow-accelerating structure (16, 51) having an inlet (26) and an outlet (28). The inlet of the flow-accelerating structure is fluidly coupled to receive a flow of combustion gases from a combustor outlet. At least one fuel injector (32, 64, 66) is disposed between the inlet and the outlet of the flow-accelerating structure. The flow-accelerating structure causes an increasing speed to the flow of combustion gases, and, as a result, the flow of combustion gases in the flow-accelerating structure experiences a decreased static temperature and a reduced combustion residence time, each of which is effective to reduce NOx emissions at the high firing temperatures of the turbine engine.