THE MECHANICAL properties of ceramic matrices uniaxially reinforced with strong continuous fibers depend on a wide variety of material parameters: the fiber and matrix elastic moduli, the matrix toughness, the statistical fiber strength, the fiber radius and fill fraction, and the sliding resistance tau between the fibers and the matrix. A major contribution to the work of fracture is the work to pull-out broken fibers from the matrix against the sliding resistance. Recent analytic theories of the pull-out predict finite pull-out for very narrow fiber strength distributions, in contrast to prior theories and ideas suggesting zero pull-out. The theories also assume that fiber cracking is distributed throughout the composite and not localized to some narrow region; such strain localization could modify composite properties tremendously. Here, both analytical arguments and numerical simulations are used to show that finite pull-out does exist for narrow fiber strength distributions. The numerical simulations also demonstrate that strain localization does occur, but that it (i) does not affect the ultimate tensile strength, and (ii) reduces pull-out only slightly but with the detailed trends in pull-out properties predicted by the analytic theory retained. Some basic tenets and results of the analytic models are thus robust and so the analytic models should serve as powerful tools for composite optimization.