A comparative study of joint distributions of wave height and period, as well as wave height and steepness, is presented. The analysis includes two theoretical joint distributions of wave height and wave period. These two distributions are transformed into joint distributions of wave height and wave steepness. The theoretical distributions are compared with measured data, as well as parametric models which are obtained by fitting to the data. The data used for comparison are relatively broad-banded and are obtained from measurements in deep waters on the Norwegian continental shelf. It is found that the theoretical distributions are inadequate to describe the joint distributions of the primary wave characteristics of these broad-band data, and thus it is suggested to use parametric models to describe such data. Finally, the engineering relevance of the joint distribution of wave height and wave steepness is discussed.