The high-pressure structural behavior of the binary intermetallic compounds CoSn, FeSn, and NiIn with the peculiar void containing CoSn ͑B35͒-type structure has been studied by means of room-temperature diamond anvil cell and high-temperature multianvil experiments, as well as by first-principles calculations. All three compounds remain structurally stable at pressures up to at least 25 GPa, whereas first-principles calculations predict high-pressure structural changes below 20 GPa. A plausible explanation for the discrepancy is that at room temperature, a sizable activation barrier inhibits kinetically the transformation into more close-packed polymorphs. It is supported by our experiments at temperatures around 1000°C and a pressure of 10 GPa. At these conditions, NiIn transforms into the temperature-quenchable stoichiometric CsCl-type high-pressure phase, which has been predicted in our first-principles calculations. However, CoSn and FeSn decompose into a mixture of compounds richer and poorer in tin, respectively. Nevertheless, it might be possible that lower temperatures and higher pressures may afford theoretically predicted polymorphs. In particular, a phase transformation to the FeSi-type structure predicted for CoSn is of interest as materials with the FeSi-type structure are known for unusual thermal and transport properties.