Narrow bandwidth and large group velocity (v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> ) dispersion are two fatal limitations of slow light in Bragg fibers. In this paper, by introducing a well-designed defect layer into the cladding of the Bragg fiber, the modal characteristics are modified by the coupling between the core mode and the defect mode. The defect location mainly determines the coupling strength and, thus, exerts a strong influence on v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> and dispersion. The defect thickness mainly determines the resonant wavelength of the defect waveguide and, thus, the wavelength where the modal coupling takes place. Consequently, the two limitations of the slow-light propagation in the Bragg fiber are overcome through proper optimization of the defect parameters. Around 1550 nm, a slow-light bandwidth up to 90 nm is achieved at an average v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> of c/5 (c is the light velocity in a vacuum) under N = 2, whereas an average v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> of c/10 is achieved with a bandwidth of 20 nm under N = 5. On the other hand, the slow-light propagation of v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> = 0.074c with both zero dispersion and zero dispersion slope is achieved, which is able to support applications requiring a subterahertz bandwidth of optical pulse. All of the fiber designs ensure sufficient low losses and good optical field distribution. The results are helpful in developing various Bragg-fiber-based slow-light devices.