We used the cumulative misfit method to divide a data set with heterogeneous stress orientations into subsets with homogeneous stress directions. We propose that slope changes of the cumulative misfit as a function of earthquake number pinpoint the boundaries of homogeneous stresses. Using a synthetic data set of 50 fault plane solutions, composed of two halves corresponding to two incompatible stress tensors, we tested the validity and efficacy of the cumulative misfit method. Our acceptance criteria for results of stress tensor inversions are (1) the directions must be well constrained, that is, the 95% confidence regions of the greatest and least principal stresses do not overlap and (2) there must be evidence for homogeneity in the sample, that is, the average misfit of the inversion is less than 6¿. We estimated stress directions in the Alaska Wadati-Benioff Zone (WBZ) using 470 fault plane solutions, which we determined for earthquakes with ML~3, and 67 published fault plane solutions for earthquakes with Ms~5. We succeeded in subdividing the data set of the small and large earthquakes into 25 and 3 subsets, with the average misfit ranging from 3.2¿ to 5.5¿. The average misfits of the subsets we accept as satisfying the assumption of homogeneity are smaller than the average misfit of the overall data set (F~10¿) by factors of 2 to 3. We estimated the stress fields at two scales along the Alaska WBZ. The stress directions measured by the large earthquakes (Ms~5) were homogeneous over large volumes, with extension downdip and the direction of greatest compression along strike. This unusual orientation of the greatest principal stress is attributed to the bend of the slab under central Alaska, which generates compressive stresses along strike. The stress orientations revealed by small earthquakes, in contrast, exhibited a great deal of heterogeneity as a function of space, although their general trend confirms the overall stress directions obtained from the large events. We propose that the ratio of the dimensions of the stress field sensed by earthquakes to the rupture dimensions is about 20 to 50. The estimated stress directions of the crustal earthquakes corresponded to the following mechanisms: (1) strike-slip faulting with greatest principal stress oriented N-S near Fairbanks and (2) thrusting with the greatest principal stress oriented NW-SE near Mount McKinley.¿ 1997 American Geophysical Union