  The analysis of tagged B_s -> J/psi phi decays determines the CP phase phi_s
in B_s-anti-B_s mixing with a two-fold ambiguity. The solutions differ in the
sign of cos(phi_s) which equals the sign of the width difference Delta Gamma_s
among the two B_s mass eigenstates. We point out that this ambiguity can be
removed with the help of B_s -> D_s K decays. We compare untagged and tagged
strategies and find the tagged analysis more promising. The removal of the sign
ambiguity in Delta Gamma_s can be done with relatively low statistics and could
therefore be a target for the early stage of B_s -> D_s K studies.
