  Dilute superconductivity survives in bulk strontium titanate when the Fermi
temperature falls well below the Debye temperature. Here, we show that the
onset of the superconducting dome is dopant-dependent. When mobile electrons
are introduced by removing oxygen atoms, the superconducting transition
survives down to $2 \times 10^{17}$ cm$^{-3}$, but when they are brought by
substituting Nb with Ti, the threshold density for superconductivity is an
order of magnitude higher. Our study of quantum oscillations reveals a
significant difference in the band dispersion between the dilute metals made by
these doping routes and our band calculations demonstrate that the rigid band
approximation does not hold when mobile electrons are introduced by oxygen
vacancies. We identify the band sculpted by theses vacancies as the exclusive
locus of superconducting instability in the ultra-dilute limit.
