Let \({S_x} = M(\left\langle x \right\rangle ;\text{I},\Lambda ;P)\) be a completely simple semigroup where \(\left\langle x \right\rangle \) is an ordered cyclic group with \(x > 1\), \({p_{11}} = {x^{ - 1}}\) and I, \(\Lambda \) are ordered, each with smallest element, \(|\text{I}|,|\Lambda | \geqslant 2\). The authors continue their investigation, started in [Commun. Algebra 29, No. 8, 3477–3494 (2001; Zbl 0993.06008)], of orders induced on \({S_x}\) by orders on I, \(\left\langle x \right\rangle\), \(\Lambda \).