  We present a measurement of the top quark mass ($m_t$) in $p\bar{p}$
collisions at $\sqrt{s} = 1.96$ TeV using $t\bar{t}$ events with two leptons
($ee$, $e\mu$, or $\mu\mu$) and accompanying jets in $4.3 fb^{-1}$ of data
collected with the D0 detector at the Fermilab Tevatron collider. We analyze
the kinematically underconstrained dilepton events by integrating over their
neutrino rapidity distributions. We reduce the dominant systematic
uncertainties from the calibration of jet energy using a correction obtained
from $t\bar{t}$ events with a final state of a single lepton plus jets. We also
correct jets in simulated events to replicate the quark flavor dependence of
the jet response in data. We measure $m_t = 173.7 \pm 2.8\thinspace(\rm stat)
\pm 1.5\thinspace(\rm syst)$ GeV and combining with our analysis in 1 fb$^{-1}$
of preceding data we measure $m_t = 174.0 \pm 2.4\thinspace(\rm stat) \pm
1.4\thinspace(\rm syst)$ GeV. Taking into account statistical and systematic
correlations, a combination with the D0 matrix element result from both data
sets yields $m_t = 173.9 \pm 1.9\thinspace(\rm stat) \pm 1.6\thinspace(\rm
syst)$ GeV.
