Glass fragments from three different hyaloclastites have been used to evaluate the range of cooling rates experienced by undersea volcanic deposits. We found that the glass fragments retain structures with a range of apparent quench rates from 25 to 0.15 K min–1. The most rapid cooling rates are interpreted to be those resulting from cooling of the lava near the water interface. Simple conductive cooling models produce a range of quench rates comparable to those of the more rapidly cooled samples. The very slow apparent quench rates are unlikely to result from simple linear cooling through the glass transition, because of the onset of crystallization; instead, they are indicators of a more complex thermal history that involves the annealing of glasses at temperatures within the glass transition interval for a dwell time sufficient to allow the relaxation of the glass to lower temperature structures. The thermal history recorded in these samples illustrates the complexity of eruptive processes and demonstrates that quench rates for natural glasses retain information relevant to more complex cooling models.