A congruence  on a semigroup S is called perfect if (a)(b) = (ab) for all a; b 2 S, as sets, and a semigroup S is said to be -idempotent-surjective (respectively perfect) if every -class of S contains an idempotent of S, where  is the least semilattice congruence on S (respectively if each congruence on S is perfect). We describe the least Clifford congruence  on an -idempotent-surjective perfect semigroup S. In addition, a characterization of all Clifford congruences on such a semigroup is given.Furthermore, we find necessary and sufficient conditions for  to be idempotent pure or E-unitary. Moreover, we give a full description of all USG-congruences on an-idempotent-surjective perfect semigroup S. In fact, we show that each USG-congruence # on S is the intersection of a semilattice congruence " and a group congruence  (and vice versa), and this expression is unique. Also, S=# = S="  S=. Finally, we investigate the lattice of Clifford congruences on a semigroup S which is a semilattice S= of E-inversive semigroups e (e 2 ES).