Experiments have been performed which demonstrate that the directional distribution of reflected thermal radiation for moderate to large angles of incidence is not intermediate to the specular and diffuse limits as commonly assumed. Indeed, for such angles of incidence on roughened surfaces, maxima in the reflected intensity distribution occur at polar angles larger than the specular angle. In some cases, the intensity of this off-specular maximum is three or four times the intensity in the specular-ray direction. The materials studied were aluminum, nickel, copper, a nickel-copper alloy, and magnesium-oxide ceramic, thereby encompassing both metals and nonmetals. Controlled surface roughnesses of 0.23 to 5.8 microns were employed over a wavelength range extending from 0.5 to 6 microns. The angle of incidence was varied from 10 to 75 deg, while reflected radiation was collected in the plane of incidence at polar angles ranging from 0 to 89 deg. The experimental results are arranged on the basis of a surface-roughness-to-wavelength ratio, σm/λ. Certain trends of the off-specular peak with incident angle and σm/λ are noted.