The Jordan type P-A,P-l of a linear form l acting on a graded Artinian algebra A over a field k is the partition describing the Jordan block decomposition of the multiplication map m(l), which is nilpotent. The Jordan degree type S-A,S-l is a finer invariant, describing also the initial degrees of the simple submodules of Ain a decomposition of A as a direct sum of k[l]-modules. The set of Jordan types of A or Jordan degree types (JDT) of A as l varies, is an invariant of the algebra. This invariant has been studied for codimension two graded algebras. We here extend the previous results to certain codimension three graded Artinian Gorenstein (AG) algebras-those of small Sperner number. Given a Gorenstein sequence T-one possible for the Hilbert function of a codimension three graded AG algebra-the irreducible variety Gor(T) parametrizes all Gorenstein algebras of Hilbert function T. We here completely determine the JDT possible for all pairs (A, l), A is an element of Gor(T), for Gorenstein sequences T of the form T = (1, 3, s(k), 3, 1) for Sperner number s = 3, 4, 5 and arbitrary multiplicity k. For s = 6 we delimit the prospective JDT, without verifying that each occurs.