  Ordinary superconductors are widely assumed insensitive to small
concentrations of random nonmagnetic impurities, whereas strong disorder
suppresses superconductivity, ultimately leading to a superconductor-insulator
transition. In between these limiting cases, a most fascinating regime may
emerge where disorder enhances superconductivity. This effect is discussed here
for the $\beta$-phase of vanadium-titanium alloys. Disorder is modeled using
the coherent potential approximation while local electronic interactions are
treated using dynamical mean-field theory. The McMillan formula is employed to
estimate the superconducting transition temperature, showing a maximum at a Ti
concentration of around $0.33$ for a local Coulomb interaction $U$ in the range
of $2$ to $3$ eV. Our calculations quantitatively agree with the experimentally
observed concentration dependent increase of $T_c$, and its maximal value of
about $20\%$.
