We attempt to answer two questions; for q greater than one, when is a simple (2q-l)-knot the branched cyclic cover of another such knot? and, for q sufficiently large to ensure the existence of an appropriate classification theorem, when is a (2q)-knot the m-twist-spin of such a knot? The methods used will be mainly algebraic, including some arising from the theory of projective modules over an integral group ring. The work is original except where references indicate otherwise; part of chapter 1 has been published previously as [St].