  We study the effects of strong coupling between a superconductor and a
semiconductor nanowire on the creation of the Majorana bound states, when the
quasiparticle dwell time in the normal part of the nanowire is much shorter
than the inverse superconducting gap. This "short junction" limit is relevant
for the recent experiments using the epitaxially grown aluminum characterized
by a transparent interface with the semiconductor and a small superconducting
gap. We find that the small superconducting gap does not have a strong
detrimental effect on the Majorana properties. Specifically, both the critical
magnetic field required for creating a topological phase and the size of the
Majorana bound states are independent of the superconducting gap. The critical
magnetic field scales with the wire cross section, while the relative
importance of the orbital and Zeeman effects of the magnetic field is
controlled by the material parameters only: $g$-factor, effective electron
mass, and the semiconductor-superconductor interface transparency.
