The strong cubic intermediate-vector-boson (IVB) model of weak interactions, based on a triplet of strong self-interacting W bosons and treating CP violation as a maximal effect at the semiweak level, is reexamined. It is shown that the basic CP=−1 semiweak interaction must possess an essentially unique structure in order to reproduce the successes of the CP-conserving universal (V,A) current-current theory. The consequences to order g3 (g is the semiweak coupling constant) of the strong cubic IVB model are worked out in detail. The most incisive test of this model at low energies is the detection of gross CP violation in ΔY=1 induced neutral-lepton-current decays of hadrons, in particular, the decays K+→π+ll¯ and KL0→μμ¯. Under certain conditions, the detection of gross CP violation may be possible in ΔY=0 W production by neutrinos on nucleons.