In the present note we prove a reduction theorem for subgroups of the general linear group GL(n, ) over a skew-field , generated by a pair of microweight tori of the same type. It turns out, that any pair of tori of residue m is conjugate to such a pair in GL(3m, ), and the pairs that cannot be further reduced to GL(3m − 1, ) form a single GL(3m, )-orbit. For the case m = 1 this leaves us with the analysis of GL(2, ), that was carried through some two decades ago by the second author, Cohen, Cuypers and Sterk. For the next case m = 2 this means that the only cases to be considered are GL(4, ) and GL(5, ). In these cases the problem can be fully resolved by (direct but rather lengthy) matrix calculations, which are relegated to a forthcoming paper by the authors.