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In this note we show that any $k$-CNF which can be refuted by aquasi-polynomial $\mathsf{Res}^*(\mathsf{polylog})$ refutation has a "narrow"refutation in $\mathsf{Res}$ (i.e., of poly-logarithmic width). We also showthe converse implication: a narrow Resolution refutation can be simulated by ashort $\mathsf{Res}^*(\mathsf{polylog})$ refutation.  The author does not claim priority on this result. The technical part of thisnote bears similarity with the relation between $d$-depth Frege refutations andtree-like $d+1$-depth Frege refutations outlined in (Kraj\'i\v{c}ek 1994,Journal of Symbolic Logic 59, 73). Part of it had already been specialized to$\mathsf{Res}$ and $\mathsf{Res}(k)$ in (Esteban et al. 2004, Theor. Comput.Sci. 321, 347).

Short $\mathsf{Res}^*(\mathsf{polylog})$ refutations if and only if narrow $\mathsf{Res}$ refutations