New computations of birelative K 2 groups and recent results on K 3 of rings of algebraic integers are combined in generalized Mayer-Vietoris sequences for algebraic k-theory. Upper and lower bounds for SK 2(ℤ G) and lower bounds for K 3(ℤ G) are deduced for G a dihedral group of square-free order, and for some other closely related groups G.