Enhancement factors for the thermonuclear reaction rates in dense bina
ry-ionic mixtures (BIMs) with charge ratio R(Z) less-than-or-equal-to
5 are calculated through detailed examination of the screening potenti
als at short ranges obtained by the Monte Carlo simulation method. Sma
ll but nonnegligible deviations of the screening distances from the co
nstant electron-density, ion-sphere scaling are discovered at R(Z) is
similar to 5 for the ''lighter'' elements; the deviations act further
to enhance the reaction rates. The triple-alpha reactions in He-C mixt
ures are treated as an example.