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Let $k$ and $k'$ be two knots in 3-sphere. Say $k$ 1--dominates $k'$, ifthere 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 finitelymany de-satellizations.  The condition of "same Gromov volume" clearly can not be removed. We alsogive a new construction of 1-domination between knots with same Gromov volumeto show that the condition "any companion of $k$ is prime" can not be removed.

On standard forms of 1--dominations between knots with same Gromov volumes