Characterizing and modeling the behavior of fading channels is critical for robust wireless systems design. This is especially the case for wireless devices designed to be positioned on the human body. So-called wearable communications are not only impacted by signal fluctuations caused by the propagation environment but also shadowed and envelope fading generated by the human body. In this paper we statistically characterize fading channels observed in wearable communications using a range of very general line of sight and multiplicative composite fading models such as K-μ / lognormal LOS and K-μ / gamma. In particular we investigate off-body wearable channels operating at 5.8 GHz for a series of experiments which are designed to be representative of everyday scenarios likely to be encountered by wearable device users. Using the Kullback-Leibler divergence, we then perform a quantitative analysis of the fits of these models to the measured composite fading data obtained for the wearable channels considered here.