Sulfur derivatives of 6,8-dioxabicyclo[3.2.1]octanes related to a number of natural products have been synthesized by the click hydrothiolation (AIBN or UV irradiation) of 7-methylene-6,8-dioxabicyclo[3.2.1]octanes, assembled from acetylene and ketones in a one-pot transition-metal-free synthetic operation. An unusual feature of this free-radical reaction is that it is accelerated in the presence of bases due to involvement of the latter in a competition between the thiol addition and proton-catalyzed isomerization of the starting bicyclooctanes.