The U.S. Air Force Three-Dimensional Nephanalysis (3DNEPH) has been employed to analyze the vertical distribution of clouds and cloud overlap statistics during January 1979 over the north Atlantic Ocean (40¿ to 60¿N). The 3DNEPH integrates both satellite and conventional observations and gives what is probably the best available information on the vertical distribution of clouds. This region was chosen because of the predominance of layered clouds and the high density of conventional observations. The grid size of the 3DNEPH is ~45 km, and the data set was additionally averaged over three different grid sizes: 90, 221, and 442 km. Three cloud overlap assumptions that have been commonly used were tested, namely the maximum, minimum, and random overlap assumptions. For adjacent layers of the 3DNEPH that contained cloud the maximum overlap assumption performed the best, accurately determining the total cloud cover to within the roundoff error for the layered cloud amounts in 82% of the cases. For two or three cloud layers that were separated by clear interstices the random overlap assumption performed the best overall for all resolutions, although there were systematic biases in the predicted cloud fraction which depend on the cloud fraction of the layers and on grid size. For grid sizes ≥90 km, random overlap resulted in a systematic underestimation of total cloud cover, ~5%. Random overlap performed worst when there were two layer with intermediate cloud fractions (30--70%). The results of this study indicate that while random overlap performs reasonably well on average, the systematic bias (which depends on grid resolution) and random discrepancies could result in significant errors when this approximation is used in general circulation modeling and cloud climatologies. ¿ American Geophysical Union 1989