  Recent evidence for a charge-Kondo effect in superconducting samples of
Pb$_{1-x}$Tl$_x$Te [1] has brought renewed attention to the possibility of
negative U superconductivity in this material, associated with valence
fluctuations on the Tl impurity sites [2]. Here, we use indium as an
electron-donor to counterdope Pb$_{.99}$Tl$_{.01}$Te and study the effect of
the changing chemical potential on the Kondo-like physics and on the
superconducting critical temperature, $T_c$. We find that, as the chemical
potential moves away from the value where superconductivity, Kondo-like
physics, and chemical potential pinning are expected, both $T_c$ and the
low-temperature resistance anomaly are suppressed. This provides further
evidence that both the superconductivity and the Kondo-like behavior are
induced by the same source, as anticipated in the negative U model.
