The present disclosure is directed to a radially stacked fuel injection module for a segmented annular combustion system. The fuel injection module includes a bundled tube fuel nozzle portion and a plurality of fuel injection lances. In one instance, a first set of fuel injection lances and a second set of fuel injection lances share a housing with the bundled tube fuel nozzle. The first and second sets of fuel injection lances are radially stacked, each set of lances being in communication with a respective injector fuel plenum. The fuel injection lances deliver fuel to a respective premixing channel formed between the side walls of an integrated combustor nozzle, an aft end of which defines a turbine nozzle. In another instance, the bundled tube fuel nozzle may be provided as a radially inner fuel nozzle and a radially outer fuel nozzle, each with a respective bundled tube fuel plenum.