Building reliable LLM agents requires decisions at two levels: the graph (which modules exist and how information flows) and the configuration of each node (models, prompts, tools, control knobs). Most existing optimizers tune configurations while holding the graph fixed, leaving structural failure modes unaddressed. We introduce Maestro, a framework-agnostic holistic optimizer for LLM agents that jointly searches over graphs and configurations to maximize agent quality, subject to explicit rollout/token budgets. Beyond numeric metrics, Maestro leverages reflective textual feedback from traces to prioritize edits, improving sample efficiency and targeting specific failure modes. On the IFBench and HotpotQA benchmarks, Maestro consistently surpasses leading prompt optimizers--MIPROv2, GEPA, and GEPA+Merge--by an average of 12%, 4.9%, and 4.86%, respectively; even when restricted to prompt-only optimization, it still leads by 9.65%, 2.37%, and 2.41%. Maestro achieves these results with far fewer rollouts than GEPA. We further show large gains on two applications (interviewer & RAG agents), highlighting that joint graph & configuration search addresses structural failure modes that prompt tuning alone cannot fix.