  We propose algorithms for determining both lower and upper bounds for the
energy barriers encountered by a flux line in moving through a two-dimensional
random potential. Analytical arguments, supported by numerical simulations,
suggest that these bounds scale with the length $t$ of the line as $t^{1/3}$
and $t^{1/3}\sqrt{\ln t}$, respectively. This provides the first confirmation
of the hypothesis that barriers have the same scaling as the fluctuation in the
free energy. \pacs{PACS numbers: 74.60.Ge, 05.70.Ln, 05.40.+j}
