We present a new strategy to explore New Physics contributions to leptonic and semileptonic $B$ decays. Using available measurements we put constraints on the Wilson coefficients of the usual model-independent low-energy effective Hamiltonian; general considerations on New Physics models are made, too. We devote particular attention to the effect of CP-violating phases of the short-distance coefficients, and provide predictions for the branching ratios that have not yet been measured.