The dynamics of spin-lattice relaxation (SLR) of metal-organic Pt(II) compounds is studied. Often such systems are characterized by pronounced zero-field splittings of the lowest-lying triplets. Previous expressions for the Orbach SLR process do not allow proper treatment of such splitting patterns. We discuss the behavior of a modified Orbach expression for a model system. Further, we present results of a fit of the temperature dependence of the SLR rate for Pt(2-thpy)(2) based on the modified expression.