Understanding the optimization objectives that shape shoot architectures remains a critical problem in plant biology. Here, we performed 3D scanning of 152 Arabidopsis shoot architectures, including wildtype and 10 mutant strains, and we uncovered a design principle that describes how architectures make trade-offs between competing objectives. First, we used graph-theoretic analysis to show that Arabidopsis shoot architectures strike a Pareto optimal that can be captured as maximizing performance in transporting nutrients and minimizing costs in building the architecture. Second, we identify small sets of genes that can be mutated to shift the weight prioritizing one objective over the other. Third, we show that this prioritization weight feature is significantly less variable across replicates of the same genotype compared to other common plant traits (e.g., number of rosette leaves, total volume occupied). This suggests that this feature is a robust descriptor of a genotype, and that local variability in structure may be compensated for globally in a homeostatic manner. Overall, our work provides a framework to understand optimization trade-offs made by shoot architectures and provides evidence that these trade-offs can be modified genetically, which may aid plant breeding and selection efforts.