  We present a Monte Carlo generator that implements significant theoretical
improvements in the simulation of top-quark pair production and decay at the
LHC. Spin correlations and off-shell effects in top-decay chains are described
in terms of exact matrix elements for $p p \to
\ell^+\nu_{\scriptscriptstyle\ell}\, l^-\bar{\nu}_{\scriptscriptstyle l} b
\bar{b}$ at NLO QCD, where the leptons $\ell$ and $l$ belong to different
families, and $b$ quarks are massive. Thus, the contributions from $t\bar{t}$
and $Wt$ single-top production as well as their quantum interference are fully
included. Matrix elements are matched to the Pythia8 parton shower using a
recently proposed method that allows for a consistent treatment of resonances
in the POWHEG framework. These theoretical improvements are especially
important for the interpretation of precision measurements of the top-quark
mass, for single-top analyses in the $Wt$ channel, and for $t\bar{t}$ and $Wt$
backgrounds in the presence of jet vetoes or cuts that enhance off-shell
effects. The new generator is based on a process-independent interface of the
OpenLoops amplitude generator with the POWHEGBOX framework.
