We present the first modern volcanological study of a subglacial-to-emergent rhyolite tuya, at SE Rauðufossafjöll, Torfajökull, Iceland. A flat-topped edifice with a volume of ~1 km3 was emplaced in Upper Pleistocene time beneath a glacier >350 m thick. Although it shares morphological characteristics with basaltic tuyas, the lithofacies indicate a very different eruption mechanism. Field observations suggest that the eruption began with vigorous phreatomagmatic explosions within a well-drained ice vault, building a pile of unbedded ash up to 300 m thick. This was followed by a subaerial effusive phase, in which compound lava flows were emplaced within ice cauldrons. Small-volume effusive eruptions on the volcano flanks created several lava bodies, with a variety of features (columnar-jointed sides, subaerial tops, peperitic bases) that are used to reconstruct spatially-heterogeneous patterns of volcano-ice interaction. Volcaniclastic sediments exposed in a stream section provide evidence for channelised meltwater drainage and fluctuating depositional processes during the eruption. We develop models for the evolution of SE Rauðufossafjöll, and discuss the differences between subglacial rhyolitic and basaltic eruption mechanisms, which are principally caused by contrasting hydrological patterns.