Abundant pumice fragments occur in the Apache Leap Tuff of east-central Arizona, an ash-flow sheet with a maximum thickness of 600 m and a K-Ar age of 20 m.y. The amount of flattening of pumice fragments is widely variable at any particular locality, but systematic measurements show that the mean degree of flattening, defined as the “flattening ratio,” steadily increases from the top downward into the body of the sheet. Ultimately the fragments are so compacted that they lose their identity. On a logarithmic scale the plot of flattening ratios is approximately linear relative to depth of burial. The uniform downward increase in flattening combines with evidence obtained from zoning and specific gravity characteristics to show that most of the deposit is a single cooling unit. Because of the uniform trend, flattening also provides a guide to the original thickness of overlying tuff at localities at which fragments can be measured. This permits the development of stratigraphy for the seemingly uniform deposit and provides a means to estimate pre-erosion thickness of the ash-flow sheet and the amount of stratigraphic throw on faults. A mining company used flattening ratios to predict successfully the ash-flow thickness cut by a new shaft. Postemplacement crystallization and diagenetic processes have greatly reduced the initial porosity of the deposit, and present porosity values erroneously indicate a considerably higher degree of welding than is inferred from deformation of the pumice fragments. It seems that in deposits where crystallization and diagenesis have been significant, flattening ratios of pumice fragments may be a better guide than porosity to the degree of welding that occurred during cooling of the deposit. The change of flattening ratio with depth can also serve as an approximate guide to the relative viscosity of pumice during emplacement. Viscosity is determined chiefly by temperature, chemical composition, volatile content, and crystallinity. The downward change in flattening ratio in the Apache Leap Tuff is gradual, indicating a relatively high viscosity. By assuming high volatile content and low groundmass crystallinity at the time of emplacement, the high viscosity can be ascribed to the combined result of nonperalkalic chemical composition and relatively low temperature.