Emergent software systems are assembled from a collection of small code blocks, where some of those blocks have alternative implementation variants; they optimise at run-time by learning which compositions of alternative blocks best suit each deployment environment encountered. In this paper we study the automated synthesis of new implementation variants for a running system using genetic improvement (GI). Typical GI approaches, however, rely on large amounts of data for accurate training and large code bases from which to source genetic material. In emergent systems we have neither asset, with sparsely sampled runtime data and small code volumes in each building block. We therefore examine two approaches to more effective GI under these constraints: the synthesis of data from sparse samples to construct statistically representative larger training corpora; and the synthesis of code to counter the relative lack of genetic material in our starting population members. Our results demonstrate that a mixture of synthesised and existing code is a viable optimisation strategy, and that phases of increased synthesis can make GI more robust to deleterious mutations. On synthesised data, we find that we can produce equivalent optimisation compared to GI methods using larger data sets, and that this optimisation can produce both useful specialists and generalists.