We experiment an alternative routing scheme for the Robust Network Loading problem. Named k-adaptive, it is based on the fact that the decision-maker chooses k second-stage solutions and then commits to one of them only after realization of the uncertainty. This routing scheme, with its corresponding k-partition of the uncertainty set, is dynamically defined under an iterative method to sequentially improve the solution. The method has an inherent characteristic of multiplying the number of variables and constraints after each iteration, so that additional measures are introduced in the solution strategy in order to control its tractability. We compare our k-adaptive results with the ones obtained through other routing schemes and also verify the effectiveness of the methods utilized using several realistic instances from SNDlib.