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A climate-glacier model was used to reconstruct Late-glacial climate conditions from two case-study glaciers at 18 degrees and 22 degrees S in the arid (sub) tropical western Andes of northern Chile. The model uses (i) the geometry of the Late-glacial maximum glaciation, (ii) modern diurnal and annual cycles, amplitudes and lapse rates of the climate, (iii) empirical-statistical sublimation, melt and accumulation models developed for this area, and (iv) dynamic ice flow through two known cross-sections for steady-state conditions. The model is validated with modern conditions and compares favorably with the glaciological features of today. The mass-balance model calculates the modern equilibrium-line altitude at 180 S as high as 5850 m (field data 5800 m), whereas no glaciers exist in the fully arid southern area at 22 degrees S despite altitudes above 6000 m and continuous permafrost. For Late-glacial times, the model results suggest a substantial increase in tropical summer precipitation (DeltaP = +840 (-50/+10) mm a(-1) for the northern test area; +1000 (-10/+30) mm a(-1) for the southern test area) and a moderate temperature depression (DeltaT = -4.4 (-0.1/+0.2) degreesC at 18 degrees S; -3.2 (+/-0.1) degreesC at 22 degrees S). Extratropical frontal winter precipitation (June-September) was <15% of the total annual precipitation. A scenario with higher winter precipitation from the westerlies circulation belt does not yield a numerical solution which matches the observed geometry of the glaciers. Therefore, we conclude that an equatorward displacement of the westerlies must be discarded as a possible explanation for the late Pleistocene glaciation in the Andes of northern Chile.