A leading-power factorization formula for weight functions relating the B̅X_sγ photon spectrum to arbitrary partial decay rates in B̅X_u l⁻ is derived. These weight functions are independent of the hadronic shape function and allow for the determination of |V_ub| in a model-independent way. We calculate the weight function in renormalization-group improved perturbation theory to complete next-to-next-to leading order at the jet scale μ_i² ∼ m_bΛ_QCD and to next-to leading order at the hard scale μ_h ∼ m_b. First-order power corrections are also included, where a model-dependence enters via the appearance of subleading hadronic shape functions.