We discuss all contributions from the Zweig-rule-satisfying SU͑3͒-breaking final state interactions ͑FSIs͒ in the B→ PP decays ͑neglecting charmed intermediate states͒, where PPϭ, K, KK , (Ј), and K(Ј). First, the effects of SU͑3͒ breaking in rescattering through Pomeron exchange are studied. Then, after making a plausible assumption concerning the pattern of SU͑3͒ breaking in non-Pomeron FSIs, we give general formulas for how the latter modify short-distance ͑SD͒ amplitudes. In the SU͑3͒ limit, these formulas depend on three effective parameters characterizing the strength of all non-Pomeron rescattering effects. We point out that the experimental bounds on the B→K ϩ K Ϫ branching ratio may limit the value of only one of these FSI parameters. Thus, the smallness of the B→K ϩ K Ϫ decay rate does not imply negligible rescattering effects in other decays. Assuming a vanishing value of this parameter, we perform various fits to the available B→ PP branching ratios. The fits determine the quark-diagram SD amplitudes, the two remaining FSI parameters and the weak angle ␥. While the set of all B→ PP branching ratios is well described with ␥ around its expected standard model ͑SM͒ value, the fits permit other values of ␥ as well. For a couple of such good fits, we predict asymmetries for the B→K, ϩ (Ј), K ϩ (Ј) decays as well as the values of the CP-violating parameters S and C for the time-dependent rate of B 0 (t)→ ϩ Ϫ . Apart from a problem with the recent B ϩ → ϩ asymmetry measurement, comparison with the data seems to favor the values of ␥ in accordance with SM expectations.