Let G be a discrete group and (G, G+) be a quasi-ordered group. Set G0+ = G+∩(G+)−1 and G1 = (G+[setmn ]G0+)∪{e}. Let [Fscr]G1(G) and [Fscr]G+(G) be the corresponding Toeplitz algebras. In the paper, a necessary and sufficient condition for a representation of [Fscr]G+(G) to be faithful is given. It is proved that when G is abelian, there exists a natural C*-algebra morphism from [Fscr]G1(G) to [Fscr]G+(G). As an application, it is shown that when G = ℤ2 and G+ = ℤ+ × ℤ, the K-groups K0([Fscr]G1(G)) ≅ ℤ2, K1([Fscr]G1(G)) ≅ ℤ and all Fredholm operators in [Fscr]G1(G) are of index zero.