Beneath most overcasts, clouds' motions and rapidly changing optical depths complicate mapping their angular distributions of luminance L v and visible-wavelength radiance L. Fisheye images of overcast skies taken with a radiometer-calibrated digital camera provide a useful new approach to solving this problem. Maps calculated from time-averaged images of individual overcasts not only show their brightness distributions in unprecedented detail, but they also help solve a long-standing puzzle about where brightness maxima of overcasts are actually located. When combined with simulated radiance distributions from MODTRAN4, our measured radiances also let us estimate the gradients of cloud thickness observed in some overcasts.