Fast-adapting type 1 (FA-1) and slow-adapting type 1 (SA-1) first-order neurons in the human tactile system have distal axons that branch in the skin and form many transduction sites, yielding receptive fields with many highly sensitive zones or 'subfields'. We previously demonstrated that this arrangement allows FA-1 and SA-1 neurons to signal the geometric features of touched objects, specifically the orientation of raised edges scanned with the fingertips. Here we show that such signaling operates for fine edge orientation differences (5-20°) and is stable across a broad range of scanning speeds (15-180 mm/s); that is, under conditions relevant for real-world hand use. We found that both FA-1 and SA-1 neurons weakly signal fine edge orientation differences via the intensity of their spiking responses and only when considering a single scanning speed. Both neuron types showed much stronger edge orientation signaling in the sequential structure of the evoked spike trains and FA-1 neurons performed better than SA-1 neurons. Represented in the spatial domain, the sequential structure was strikingly invariant across scanning speeds, especially those naturally used in tactile spatial discrimination tasks. This speed invariance suggests that neurons' responses are structured via sequential stimulation of their subfields and thus links this capacity to their terminal organization in the skin. Indeed, the spatial precision of elicited action potentials rationally matched spatial acuity of subfield arrangements, which corresponds to a spatial period similar to the dimensions of individual fingertip ridges.