  Several theoretical analyses of the two superconducting energy gaps of
magnesium diboride, $\Delta_\pi$ and $\Delta_\sigma$, predict substructures
within each energy gap, rather than two pure numbers. Recent experiments have
revealed similar structures. We report tunneling conductance data providing
additional experimental evidence for these features. The absence of these
features in c-axis tunneling, and a sharp peak in the subgap (associated with
the counterelectrode material), support the conclusion that these features are
intrinsic to MgB2. By demonstrating the inadequacy of a simple two-gap model in
fitting the data, we illustrate that some distinctions between theoretical
models of energy gap substructures are experimentally accessible.
