Previous work on the perception of glossy materials has mostly focused on two dimensions: gloss strength and microscale roughness. However, more advanced reflectance models often include additional parameters for controlling the distribution of reflected light. It remains unknown whether these additional dimensions have a perceptually significant influence on appearance. In particular, among the six types of gloss suggested by Hunter in his seminal book (Hunter, 1975), “haze” remains among the less studied of potentially pertinent material cues. From a physical point of view, hazy reflections are associated with heavy-tailed, or leptokurtic, reflectance functions, as often occurs in semi-polished metals or coated materials. We have investigated gloss haze by rendering movies of irregularly shaped objects made of metallic materials exhibiting more or less leptokurtic reflectance functions. We modeled hazy metals using a two-layered glossy material model with two centered Gaussian-like lobes (Ward, 1992) of different spread. Varying both the (1) relative spread and (2) relative magnitude of the two lobes yielded a 5x5 array of different materials. Subjects rated the following qualities for each material: glossiness, blurriness, haziness, coatedness, polish, and friction. Principal component analysis of the results reveals that haziness is a distinct visual dimension orthogonal to the commonly studied glossiness and blurriness. Coatedness appears to be nearly synonymous with haziness, as this is one of the main physical causes of haze in real world materials. Polish seems to be a combination of glossiness and haziness, as materials go from dull to hazy to highly glossy during the physical polishing process. The inferred tactile quality of friction is apparently uncorrelated with haziness. Our results demonstrate that haze is indeed a distinct perceptual dimension of gloss, which is systematically related to the kurtosis of the specular lobe.