We show that the ECM algorithm can always be constructed to converge at the
same or approximately the same rate as the Ehl algorithm. The construction
is based on the well-known conjugate directions algorithm. This result bot
h suggests ways of speeding up the convergence of ECM and provides a simple
way of identifying cases where the simplicity and stability of ECM over EM
is attained at effectively no loss in convergence speed. Three examples ar
e given.