It is well-known that a heavy impurity atom in a lattice of light atoms induces a lower frequency in-band resonance mode in the vibrational spectrum. The exact effect of such a mode on the lat- tice spectrum has not previously been reported and effects of such modes on superconductivity have not previously been described. Sputtered thin films of bcc Mo(,1-x)Re(,x), 0.2 0. (delta) increases with (lamda)(,R), the Re contribution to the electron-phonon coupling con- stant (lamda). The dependences of the anomalous softening and width of the resonance mode on (lamda)(,R) fit the Yu-Anderson theory of local pho- non screening by a Fermi gas of electrons treated as Tomonago;bosons. These results explain the low N(0), high T(,c) behavior of Mo(,.6)Re(,.4); *DOE Report IS-T-1246. This work was performed under contract No. W-7405-Eng-82 with the U.S. Department of Energy.