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New constructive algorithms for the two-dimensional guillotine-cutting problem are presented. The algorithms were produced from elemental algorithmic components using evolutionary computation. A subset of the components was selected from a previously existing constructive algorithm. The algorithms’ evolution and testing process used a set of 46 instances from the literature. The structure of three new algorithms is described, and the results are compared with those of an existing constructive algorithm for the problem. Several of the new algorithms are competitive with respect to a state-of-the-art constructive algorithm. A subset of novel instructions, which are responsible for the majority of the new algorithms’ good performances, has also been found.