We compare the two recently introduced semidirect product operations * r and * rr within the lattice of e-varieties of locally inverse semigroups. For each e-variety V which contains all rectangular bands and is properly contained in the e-variety of all completely simple semigroups, the inclusions
S * rr V S * r V S * rr (Aq • V)are proved where S is the e-variety of all semilattices and Aq the variety of all abelian groups of exponent dividing q where q is any integer greater than one. Some consequences for the class of finite locally inverse semigroups are also obtained.