  We compute the anomalous dimension of the third and fourth moments of the
flavour non-singlet twist-2 Wilson and transversity operators at three loops in
both the MSbar and RI' schemes. To assist with the extraction of estimates of
matrix elements computed using lattice regularization, the finite parts of the
Green's function where the operator is inserted in a quark 2-point function are
also provided at three loops in both schemes.
