We present a considerably improved analysis of model-independent bounds on new physics effects in non-leptonic tree-level decays of B-mesons. Our main finding is that contributions of about ±0.1 to the Wilson coefficient of the colour-singlet operator Q 2 of the effective weak Hamiltonian and contributions in the range of ±0.5 (both for real and imaginary part) to Q 1 can currently not be excluded at the 90% C.L.. Effects of such a size can modify the direct experimental extraction of the CKM angle γ by up to 10 • and they could lead to an enhancement of the decay rate difference ∆Γ d of up to a factor of 5 over its SM value-a size that could explain the D0 dimuon asymmetry. Future more precise measurements of the semi-leptonic asymmetries a q sl and the lifetime ratio τ (B s)/τ (B d) will allow to shrink the bounds on tree-level new physics effects considerably. Due to significant improvements in the precision of the non-perturbative input we update all SM predictions for the mixing obervables in the course of this analysis, obtaining: ∆M s = (18.77 ± 0.86) ps −1 , ∆M d = (0.543 ± 0.029) ps −1 , ∆Γ s = (9.1 ± 1.3) • 10 −2 ps −1 , ∆Γ d = (2.6 ± 0.4) • 10 −3 ps −1 , a s sl = (2.06 ± 0.18) • 10 −5 and a d sl = (−4.73 ± 0.42) • 10 −4 .