  We consider leptonic $B^-\to \ell^- \bar\nu_\ell$ and semileptonic $\bar B
\to \pi \ell^- \bar\nu_\ell$, $\bar B \to \rho \ell^- \bar\nu_\ell$ decays and
present a strategy to determine short-distance coefficients of New-Physics
operators and the CKM element $|V_{ub}|$. As the leptonic channels play a
central role, we illustrate this method for (pseudo)-scalar operators which may
lift the helicity suppression of the corresponding transition amplitudes
arising in the Standard Model. Utilising a new result by the Belle
collaboration for the branching ratio of $B^-\to \mu^- \bar\nu_\mu$, we explore
theoretically clean constraints and correlations between New Physics
coefficients for leptonic final states with $\mu$ and $\tau$ leptons. In order
to obtain stronger bounds and to extract $|V_{ub}|$, we employ semileptonic
$\bar B \to \pi \ell^- \bar\nu_\ell$ and $\bar B \to \rho \ell^- \bar\nu_\ell$
decays as an additional ingredient, involving hadronic form factors which are
determined through QCD sum rule and lattice calculations. In addition to a
detailed analysis of the constraints on the New Physics contributions following
from current data, we make predictions for yet unmeasured decay observables,
compare them with experimental constraints and discuss the impact of
CP-violating phases of the New-Physics coefficients.
