Thermal subsidence would have drowned ancient volcanic islands (DAVI). Ancient volcanoes, if active at present rates in the main ocean basins, would have produced 1.5--3 times the observed number of DAVI. Shallow-water indicators have been collected from 11% of guyots, and another 3% appear to be downed barrier reefs or atolls on relfection profiles. A minimum of 65% of DAVI lie downdrift from hot spots that generate volcanic islands. The DAVI have the same 3 to 4-km relief as the islands would have if, truncated. Nonetheless hypotheses of a constructional origin of guyots continue to be proposed. Relative to these hyphotheses are the following: (1) all four large, active submarine volcanoes that have been surveyed lack flat tops. and (2) many small, deep, inactive, relatively flat-topped volcanoes are constructional forms but none with more than 2 km of relief are known to exist. Thus it is probable that all guyots with more than 2 km of relief are DAVI, but the possible existence of larger constructional forms is not excluded. There is no evidence that guyots large enough to be of interest in studying the epeirogenic history of midplate swells are not DAVI.