Of the 56 isomorphism classes of simple groups of order up to 106there are 10 of order up to 105distinct from PSL(2,q). Presentations for these groups are given here in the form G = < a, b; a2= bm= 1, {ri(a, b)}iϵI= 1 > where m is minimal (with respect to a). They are complete in the sense that any pair (a, b) of generators of G satisfying the relations a2= bm= 1, with m minimal, will satisfy the defining relations of just one presentation listed here.