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.
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