Modern software deployment process produces software that is uniform and hence vulnerable to large-scale code-reuse attacks, such as Jump-Oriented Programming (JOP) attacks. Compiler-based diversification improves the resilience of software systems by automatically generating different assembly code versions of a given program. Existing techniques are efficient but do not have a precise control over the quality of the generated variants. This paper introduces Diversity by Construction (DivCon), a constraint-based approach to software diversification. Unlike previous approaches, DivCon allows users to control and adjust the conflicting goals of diversity and code quality. A key enabler is the use of Large Neighborhood Search (LNS) to generate highly diverse code efficiently. For larger problems, we propose a combination of LNS with a structural decomposition of the problem. To further improve the diversification efficiency of DivCon against JOP attacks, we propose an application-specific distance measure tailored to the characteristics of JOP attacks. We evaluate DivCon with 20 functions from a popular benchmark suite for embedded systems. These experiments show that the combination of LNS and our application-specific distance measure generates binary programs that are highly resilient against JOP attacks. Our results confirm that there is a trade-off between the quality of each assembly code version and the diversity of the entire pool of versions. In particular, the experiments show that DivCon generates near-optimal binary programs that share a small number of gadgets. For constraint programming researchers and practitioners, this paper demonstrates that LNS is a valuable technique for finding diverse solutions. For security researchers and software engineers, DivCon extends the scope of compiler-based diversification to performance-critical and resource-constrained applications.