Let S be a finite semigroup. The paper under review studies units of the semigroup ring ZS over the integers. Suppose QS does not have an epimorphic image which is a 2×2 matrix ring over Q or a quadratic imaginary extension of Q or a noncommutative division ring. Assume that if G is a maximal subgroup of S with QG and QS having isomorphic noncommutative simple image, then G has no non-abelian fixed-point free homomorphic image. Let U be the group generated by Bass cyclic units, bicyclic units, or units of the form 1+x where x is running through some finite multiplicatively closed set of additive generators of the radical of ZS. Then, U is of finite index in the unit group of ZS.