A model for sedimentation from turbulent suspensions predicts that tephra concentration decreases exponentially with time in an ascending volcanic column and in the overlying umbrella cloud. For grain-size distributions typical of plinian eruptions application of the model predicts for thickness variations in good agreement with the exponential thinning observed in tephra fall deposits. The model also predicts a proximal region where fallout from the plume margins results in a more rapid decrease in thickness so that the deposit shows two segments on a thickness versus distance plot. Several examples of deposits with two segments are known. The distance at which the two segments intersect is a measure of eruption column height. The thickness half-distance (∼ equivalent to the dispersal index of Walker) is strongly correlated with column height, but is also weakly dependent on grain-size distribution of the ejecta. For a dispersal index of 500 km2 (the plinian/subplinian boundary of Walker) column heights between 14 and 18 km are calculated. For ultraplinian deposits with D>50000 km2 column heights of at least 45 km are implied. Model grain-size distributions of the deposits have sorting values comparable to those observed in tephra fall deposits formed from eruption columns in a weak or negligible cross-wind. Median diameter decreases exponentially with distance as is observed. Sorting (σφ) improves with distance as is observed in plinian deposits in a weak wind. However, tephra fall deposits formed in strong winds do not show improved sorting with distance and proximal deposits are typically somewhat better sorted than the model calculations. Differences are attributed to the influence of wind which disperses particles further than predicted in our model and which has an increasing influence as particle size decreases.