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We explore the range of values of the in-medium width of a $\rho$-meson atrest which is compatibale with the QCD sum rule approach in a nuclear mediumassuming vector meson dominance and a Brown-Rho scaling law of the $\rho$-mesonmass with the chiral condensate. The lower and upper bounds for the in-mediumwidth are found to be strongly increasing with the decreasing mass of the$\rho$-meson (increasing nuclear density). We also study the bounds for thein-medium width in models not satisfying the Brown-Rho scaling law. It is shownthat the in-medium width depends on how rapidly the mass decreases incomparison to the change of the quark condensate. The bounds for the in-mediumwidth increase with density only if the relative change of the quark condensateis stronger than the relative decrease in mass. This is important forexperimental tests of the Brown-Rho scaling paradigm and other dropping$\rho$-mass scenarios.Comment: Revised and extended version. In this version we also study the  in-medium width for decreasing $\rho$-masses in models that do not satisfy  the Brown-Rho scalin la

Mass and width of the ρ-meson in a nuclear medium from Brown-Rho scaling and QCD sum rules