This study provides new classes of nonseparable space-time covariance functions with spatial (or temporal) margins that belong to the generalized Wendland class of compactly supported covariance functions. An interesting feature of our covariances, from a computational viewpoint, is that the compact support is a decreasing function of the temporal (spatial) lag. We provide conditions for the validity of the proposed class, and analyze the problem of differentiability at the origin for the temporal (spatial) margin. A simulation study explores the finite-sample properties and the computational burden associated with the maximum likelihood estimation of the covariance parameters. Finally, we apply the proposed covariance models to Irish wind speed data, and compare the results with those of Gneiting-Matérn models in terms of fitting, prediction efficiency, and computational burden. The necessary and sufficient conditions, together with other results on dynamically varying compact supports, are provided in the online Supplementary Material.