Single-aliquot (U-Th)/He dating of iron-oxides requires less mass and has a higher spatial resolution than the two-aliquot approach, and is, therefore, a more reliable tool for quantifying the timescales of weathering processes, fault activity, and the development of soils and surfaces. Highly helium-retentive hematite samples must be heated to 1000-1100 °C to completely degas He, but we show that U is lost progressively during laser-heating starting at ~900 °C, with major U-loss at ~980 °C and complete U-loss at 1050-1100 °C. This partial or complete loss of U leads to incorrect (U-Th)/He ages that appear older than the true ages. We performed a series of heating tests on hematite and goethite aliquots with independently determined (U-Th)/He ages of 10-1761 Ma in which the helium release was determined by isotope-dilution mass spectrometry and phase change was monitored by infrared spectroscopy. As hematite is heated, reduction of Fe3+ causes a phase change to magnetite and then to elemental Fe. We correlate the onset of U-loss to the phase change from hematite to magnetite. By raising the temperature of this phase transition using a high oxygen partial pressure (pO2) in the sample chamber during laser-heating, we show that the onset temperature of U-loss is equally raised. Samples can therefore be safely degassed at higher temperatures without any detectable U-loss. In our implementation of this technique, the O2 in the sample chamber is being withdrawn from a tank using a pipette and it is being released before and captured after the degassing process on activated charcoal in a cold finger with a movable LN2 Dewar flask. We describe the automation of this process for routine degassing of hematite samples. We show that an average age calculated on a reference hematite sample from replicate aliquots (n=12), which were analyzed using this procedure, has a relative uncertainty of 2% (1σ), and is within uncertainty of the previously measured two-aliquot age. We suggest this high-pO2 degassing procedure as a way to precisely and reproducibly determine single-aliquot hematite and goethite (U-Th)/He ages.