The transport of particles or heat against the driving gradient is studied by employing a probabilistic transport model with a characteristic particle step length that depends on the local concentration or heat gradient. When this gradient is larger than a prescribed critical value, the standard deviation of the step size is large compared to its value when the gradient is below critical. For symmetric as well as asymmetric off-axis fueling, the model is capable of producing profiles peaking at the axis. Additionally, profile consistency is obtained over a broad range of source strengths. These results supplement recent works by van Milligen [Phys. Plasmas 11, 3787 (2004)], which applied Levy distributed step sizes in the case of supercritical gradients to obtain the up-gradient transport. (c) 2005 American Institute of Physics.