Volcanic ash (fine-grained tephra) within Greenland ice cores can greatly complement the understanding of past volcanism, and its environmental and societal impacts. The presence of ash in sparse concentrations in the ice raises questions about whether such material represents primary ashfall in Greenland or resuspended (remobilised) material from continental areas. Here, we investigate this issue by examining tephra content in quasi-annual samples from two Greenland ice cores during a period of ~20-years, and considering their relationships to sulphur and particulate data from the same cores. We focus on the interval 815–835 CE as it encompasses a phase (818–822 CE) of heightened volcanogenic sulphur previously ascribed to an eruption of Katla, Iceland. We find that tephra is a frequent but not continuous feature within the ice, unlike similarly-sized particulate matter. A solitary ash shard whose major element geochemistry is consistent with Katla corroborates the attribution of the 822±1 CE sulphur peak to this source, clearly showing that a single shard can signify primary ashfall. Other tephras are present in similarly low abundances but their geochemistries are less certainly attributable to specific sources. While these tephra shards tend to coincide with elevated sulphur and fine (<10 μm) particulates, they are not associated with increased coarse (>10 μm) particle concentrations that might be expected if the shards had been transported by dust storms. We conclude that the sparse shards derive from primary ashfall and we argue that low shard abundance provides insufficient grounds to dismiss the potential significance of sparse tephras.