Many Hesperian outflow channels head at elevations compatible with aquifer recharge beneath the Martian south polar cap, and such channels are widely interpreted as the products of this recharge. Some outflow channels head at greater elevations that are inconsistent with southern recharge, including three systems located in Aurorae Planum and eastern Ophir Planum. These three systems have previously been interpreted as having formed through aqueous outbursts from local aquifers recharged by the meltwaters of ancient upland glaciers to the west. However, the viability of this interpretation is weakened by the lack of a geomorphic record supportive of past meltwater flow from western uplands, inconsistencies between hypothesized processes and the nature of regional topography and mineralogy, and the absence of satisfactory analog processes for catastrophic aqueous flow from the subsurface. In contrast, a volcanic origin for the Ophir and Aurorae systems appears to be in accord with the basic characteristics of constituent channels and associated landforms, the volcanotectonic nature of the Valles Marineris system and adjacent upland plains, and the nature of available analog landforms and processes. Though numerous uncertainties remain, a volcanic interpretation of these outflow systems can more simply account for the existence of component channels. The attributes of other elevated outflow systems on Mars similarly appear to be most consistent with volcanic origins. If the Ophir and Aurorae systems formed volcanically, thermal considerations imply minimum erupted lava volumes of 6.4 × 103 km3 for Allegheny Vallis and 6.2 × 104 km3 for Elaver Vallis.