  In doped SrTiO$_{3}$ superconductivity persists down to an exceptionally low
concentration of mobile electrons. This restricts the relevant energy window
and possible pairing scenarios. We present a study of quantum oscillations and
superconducting transition temperature, $T_{c}$ as the carrier density is tuned
from $10^{17}$ to $10^{20}$ $cm^{-3}$ and identify two critical doping levels
corresponding to the filling thresholds of the upper bands. At the first
critical doping, which separates the single-band and the two-band
superconducting regimes in oxygen-deficient samples, the steady increase of
T$_{c}$ with carrier concentration suddenly stops. Near this doping level, the
energy dispersion in the lowest band displays a downward deviation from
parabolic behavior. The results impose new constraints for microscopic pairing
scenarios.
