Impurities in the vicinity of a weak link, modeled as a ballistic supe
rconducting quantum point contact, fluctuate in rime and generate low-
frequency voltage noise. Adopting the RSJ-model giant fluctuations are
found for bias currents (I-B) slightly exceeding the critical current
(I-C). This enhanced noise level is caused by switching of a mode-qua
ntized super current - in the absence of quantization noise is vanishi
ngly small. Minimal noise is always attained at I-B = root 2I(C)(T). I
n the presence of many impurities the noise spectrum is of the form S(
omega) proportional to omega(-1+beta). The order of magnitude of the e
xponent beta is universally found to be 1/ln (Gamma(max)/Gamma(min)) w
here Gamma(max) and Gamma(min) are the maximum and minimum rates of tr
ansitions, respectively, of the impurities.