  We present a measurement of the top-quark mass in events containing two
leptons (electrons or muons) with a large transverse momentum, two or more
energetic jets, and a transverse-momentum imbalance. We use the full
proton-antiproton collision data set collected by the CDF experiment during the
Fermilab Tevatron Run~II at center-of-mass energy $\sqrt{s} = 1.96$ TeV,
corresponding to an integrated luminosity of 9.1 fb$^{-1}$. A special
observable is exploited for an optimal reduction of the dominant systematic
uncertainty, associated with the knowledge of the absolute energy of the
hadronic jets. The distribution of this observable in the selected events is
compared to simulated distributions of ${t\bar{t}}$ dilepton signal and
background.We measure a value for the top-quark mass of $171.5\pm 1.9~{\rm
(stat)}\pm 2.5~{\rm (syst)}$ GeV/$c^2$.
