To a left-cancellative semigroup, $S$, one can always associate a reduced C-algebra $C_{r}^{*}(S)$ , but it is not obvious how to attach a universal C$^{*}$-algebra to $S$. We explain a general construction that yields a candidate for a groupoid model, $G(S)$, to $C_{r}^{*}(S)$. It is obtained as a reduction of Paterson's universal groupoid attached to an inverse semigroup. The non-Hausdorff nature of $G(S)$ means that this procedure does not always work; in the talk we try to pinpoint exactly when it does and give conditions on $S$ which guarantees that it does. In this case we can use $G(S)$ to define a universal C$^{*}$-algebra of $S$.