An isomer, with t1/2 = 35 +- 10 ns and J, Kpi = 14, 14+, has been observed in the nucleus 176W using the reaction 150Nd(30Si,4n) at a beam energy of 133 MeV. The isomer exhibits an unusual pattern of decay in which the _majority_ of the flux proceeds directly to states with <K>=0, bypassing available levels of intermediate K. This severe breakdown of normal K-selection rules in 176W is compared with recent observations of K-violation in neighboring nuclei, within the framework of proposed theoretical approaches. The available data on these K-violating decays seem to have a consistent explanation in models of K-mixing which include large-amplitude fluctuations of the nuclear shape.