1. A series of experiments have been carried out with Drosophila melanogaster in order to improve further a population, highly selected for a quantitative character, by introducing genetic material from an inferior population. The effects of selecting the latter before crossing to the selected line, of waiting after crossing before restarting selection and of varying the intensity of selection after crossing have been studied. The inferior population used was the large random breeding population from which the selected line had been produced by selecting downwards for sternopleural bristles.

2. There proved to be some incompatibility between the conditions necessary to achieve the two criteria of success—the time to surpass the selected line and the extent by which it was eventually exceeded. The lines which surpassed it soonest had not been selected before crossing and had been selected intensely immediately afterwards. Those which surpassed it most had had the greatest amount of selection before crossing followed by the most intense selection afterwards.

3. Crossing-over did not appear to be a limiting factor after crossing. Neither a period of relaxation after crossing nor a lower intensity of selection after crossing increased the chance of success.

4. Genetic analyses were made of several lines which had exceeded the original selected line. In separate lines, second, third and fourth chromosomes were found which were superior to the chromosomes of the selected line. This and other evidence shows that the limits in such lines with a small number of parents are not in any way absolute but artefacts of the selection programme. The extreme third and fourth chromosomes were both recessive to that of the selected line in the effect on bristle score.

5. A theoretical discussion of such selection programmes is given, assuming that the character is controlled by independently segregating loci. It is shown that, if two alleles at different loci have an equal but small chance of fixation in the initial selection, one because it is rare and the other because, though frequent, it has little effect on the character, such a programme will tend to pick up the former rather than the latter. Of two such rare alleles with an equal initial chance of fixation, the one additive and the other recessive, the chance of fixation of the latter will be greater in a crossing programme.