We report the results of a study of the overall crystallization kinetics of a set of molecular weight and composition fractions of random ethylene copolymers. These copolymers, with ethyl and butyl branches, cover a wide range in molecular weights and co-unit contents. The influence on the crystallization process of molecular weight at a fixed co-unit content, as well as that of co-unit content at a fixed molecular weight, could be assessed by the appropriate choice of fractions. Studying the overall rate of crystallization removes the restriction of having to focus on the growth of well-defined morphological forms, such as spherulites. This latter method severely limits the range of molecular weights and copolymer compositions that can be studied. On the other hand, it has been well-established that the salient features of the crystallization process, such as the temperature coefficient and delineation of regimes, can be obtained with equal reliability by either of the two experimental methods. The most general features of the crystallization process are very similar to those of homopolymers. However, some important exceptions are found. Foremost among these is the fact that the isotherms do not superpose one with the other; deviations from the Avrami relation occur at low levels of crystallinity; and only relatively low levels of crystallinity can be attained after long-time crystallization. These phenomena can be explained by the changing composition of the melt during isothermal crystallization, the restraints that are placed on the concentration of sequences that can participate in steady-state nucleation, and the theoretical limitations on the true equilibrium crystallinity levels. Certain aspects of the crystallization process will be detailed which show that for these purposes a random copolymer behaves as if it were a homopolymer of much higher molecular weight.