We have recorded reflection profiles of firn through large areas of West Antarctica and part of the East Antarctic plateau using 400 MHz short-pulse radar. The locations show accumulation rates that vary from well above to well below the vertical radar resolution. Most reflection horizons have extensive lateral continuity, and are composed of distinctive wavelets with a consistent phase polarity sequence within their successive half-cycles. We modeled these waveforms, and conclude that they arise from thin, double layers of ice over hoar, which is consistent with the standard model of firn stratification. In addition, we conclude that ice/hoar layers are extensive throughout West Antarctica and also present (although more sparsely) beneath the Antarctic Plateau.