  A subvariety V of an abelian variety is `translate' if it is the union of
translates of proper algebraic subgroups. An irreducible V is `transverse' if
it is not contained in any translate variety. Effective sharp lower bounds for
a transverse subvarieties of a power of an elliptic curve E are known. Here, we
prove a sharp lower bound for the essential minimum of non-translate
subvarieties of such a power E^g.
