A general regenerative model of the Brayton refrigeration-cycle working with an ideal Bose-gas is used to discuss the influence of both the quantum degeneracy and regeneration on the performance of the cycle. Expressions for some important parameters, such as the refrigeration load, work input, coefficient of performance and minimum pressure-ratio, of the Brayton refrigeration-cycle are derived analytically and used to generate the refrigeration load, work input, coefficient of performance, and relative refrigeration-load versus pressure ratio curves. Moreover, several special cases are discussed in detail. The results obtained here will be helpful to reveal the performance characteristics of the Bose-Brayton refrigeration-cycle, further understand the difference and connection between the classical and quantum Brayton refrigeration-cycles, and theoretically expound the importance of the regeneration application for the Brayton refrigeration-cycle. (c) 2005 Elsevier Ltd. All rights reserved.