  One-dimensional p-wave superconductors are known to harbor Majorana bound
states at their ends. Superconducting wires with a finite width W may have
fermionic subgap states in addition to possible Majorana end states. While they
do not necessarily inhibit the use of Majorana end states for topological
computation, these subgap states can obscure the identification of a
topological phase through a density-of-states measurement. We present two
simple models to describe low-energy fermionic subgap states. If the wire's
width W is much smaller than the superconductor coherence length \xi, the
relevant subgap states are localized near the ends of the wire and cluster near
zero energy, whereas the lowest-energy subgap states are delocalized if $W
\gtrsim \xi$. Notably, the energy of the lowest-lying fermionic subgap state
(if present at all) has a maximum for W ~ \xi.
