We suggest a simple method for interpolation of data on the horizontal most compressive principal stress direction (&sgr;ˆ1h) which makes no assumptions about their distribution, except that the probability of a given discrepancy is primarily a function of distance. Using the 6000 data of the World Stress Map, we obtain empirical two-point distributions of direction differences at a number of distances. Then, to find the probability distribution at an interpolation point, we form the product of the distributions implied by all the available data within the correlation horizon (with or without preaveraging of clustered data). It is then simple to select the most likely direction and 90% (or other) confidence bounds. The resulting global maps of &sgr;ˆ1h directions have 90% confidence limits of less than ¿45¿ over 20--65% of the globe, and small uncertainties of less than ¿10¿ over 5--25% of the globe (depending on the method). Both maps illustrate how radial &sgr;ˆ1h directions encircle high topography (or unusually shallow bathymetry), suggesting a generally low level of deviatoric stress in the lithosphere. ¿ American Geophysical Union 1996