One mechanism of producing fluvial sheetsand bodies is by the amalgamation of individual channel belts by lateral migration. The lateral migration of sand-bed rivers by periodic avulsion may be assisted by more steady channel combing. Combing occurs by the preferential deposition on accretionary bars on one bank of the river, concomitant with erosion on the other side. We present descriptions and interpretations of the deposits of two different, moderately large, sand-bed rivers that produced extensive sandbodies at least in part by steady lateral migration or combing, which is evidenced by the geometry and directional properties of the preserved bedform and barform structure. Significantly, in both cases lateral migration occurred, or was preserved, in one direction only. Two basic types of model are possible to explain these phenomena. A consistent migration direction in many stacked fluvial cycles may be the product of either (1) the preferential preservation of the deposits of one migration direction in a steady-state system, or (2) perpetual combing of the formative river in one direction during repeated aggradation cycles. Type (1) is the result of position on the floodplain, possibly with a tectonic control; type (2) requires a tectonic control on the palaeomorphology of the floodplain. We prefer a model for both our examples in which tectonic tilting of the floodplain causes combing of the river towards the zone of greatest subsidence. A rise in base level occurs with tilting, and therefore the rivers are also thought to have aggraded during lateral migration thus causing a preservational bias on the directional properties of the resulting fluvial succession.