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 and security 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, such as the code size or speed, of the generated code variants. This paper introduces Diversity by Construction (DivCon), a constraint-based compiler 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 assembly 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 DivCon's combination of LNS and our application-specific distance measure generates binary programs that are highly resilient against JOP attacks (they share between 0.15% to 8% of JOP gadgets) with an optimality gap of 10%. 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 is able to generate binary programs that share a very small number of gadgets, while delivering near-optimal code. 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.