We study the phenomenology of simplified Z′ models with a global U(2)³ flavor symmetry in the quark sector, broken solely by the Standard Model Yukawa couplings. This flavor symmetry, known as less-minimal flavor violation, protects ΔF = 2 processes from dangerously large new physics (NP) effects and at the same time provides a free complex phase in b → s transitions, allowing for an explanation of the hints for additional direct CP violation in kaon decays (ϵ′/ϵ) and in hadronic B-decays (B → Kπ puzzle). Furthermore, including the couplings of the Z′ boson to the leptons, it is possible to address the intriguing hints for NP (above the 5σ level) in b → sℓ⁺ℓ^- transitions. Taking into account all flavor observables in a global fit, we find that our model can (for the first time) provide a common explanation for ϵ′/ϵ, the B → Kπ puzzle and b → sℓ⁺ℓ^- data. Sizeable CP violation in b → sℓ⁺ℓ^- observables, in particular A₈, is predicted, which can be tested in the near future, and an explanation of the B → Kπ and ϵ′/ϵ puzzles leads to effects in dijet tails at the LHC that are not far below the current limits. If we require that also b → sℓ⁺ℓ^- anomalies are explained, cancellations in dimuon tails (possibly by a second Z′) are needed to satisfy LHC data.