Snow-accumulation rates are known to be sensitive to local changes in ice-sheet surface slope because of the effect of katabatic winds. These topographic effects can be preserved in ice cores that are collected at non-ice-divide locations. The trajectory of an ice-core site at South Pole is reconstructed using measurements of ice-sheet motion to show that snow was probably deposited at places of different surface slope during the past 1000 years. Recent accumulation rates, derived from shallow firn cores, vary along this trajectory according to surface topography, so that on a relatively steep flank mean annual accumulation is similar to 18% smaller than on a nearby topographic depression. These modern accumulation rates are used to reinterpret the cause of accumulation rate variability with time in the long ice-core record as an ice-dynamics effect and not a climate-change signal. The results highlight the importance of conducting ancillary ice-dynamics measurements as part of ice-coring programs so that topographic effects can be deconvolved from potential climate signals.