The magnetic properties of small-K superconducting In-Bi, In-Tl, In-Pb, Sn-Bi, and Sn-Sb alloys are investigated. The evaluation of the experiments is carried out in the framework of BCS and GLAG theory. At a critical alloy concentration a phase transition occurs, at which type I superconductivity goes over into type II. Comparing the results with Lifshitz's theory, it is found that the phase transition is of higher than second order. The contribution from the nonanalytical part of the concentration dependence of the electronic specific heat coefficient is 0.63-0.77, and thus the order of the phase transition increases by this amount.