  Let $k$ and $k'$ be two knots in 3-sphere. Say $k$ 1--dominates $k'$, if
there is a proper degree 1 map $f\co E(k)\to E(k')$, between knot exterior of
$k_i$.
  Theorem: Suppose that any companion of $k$ is prime. If $k$ 1--dominates $k'$
with the same Gromov volume, then $k'$ can be obtained from $k$ by finitely
many de-satellizations.
  The condition of "same Gromov volume" clearly can not be removed. We also
give a new construction of 1-domination between knots with same Gromov volume
to show that the condition "any companion of $k$ is prime" can not be removed.
