Analyzing unstructured data has been a persistent challenge in data processing. Large Language Models (LLMs) have shown promise in this regard, leading to recent proposals for declarative frameworks for LLM-powered processing of unstructured data. However, these frameworks focus on reducing cost when executing user-specified operations using LLMs, rather than improving accuracy, executing most operations as-is (in a single LLM call). This is problematic for complex tasks and data, where LLM outputs for user-defined operations are often inaccurate, even with optimized prompts. For example, an LLM may struggle to identify {\em all} instances of specific clauses, like force majeure or indemnification, in lengthy legal documents, requiring decomposition of the data, the task, or both. We present DocETL, a system that optimizes complex document processing pipelines, while accounting for LLM shortcomings. DocETL offers a declarative interface for users to define such pipelines and uses an agent-based approach to automatically optimize them, leveraging novel agent-based rewrites (that we call rewrite directives), as well as an optimization and evaluation framework. We introduce (i) logical rewriting of pipelines, tailored for LLM-based tasks, (ii) an agent-guided plan evaluation mechanism that synthesizes and orchestrates task-specific validation prompts, and (iii) an optimization algorithm that efficiently finds promising plans, considering the latencies of agent-based plan generation and evaluation. Our evaluation on four different unstructured document analysis tasks demonstrates that DocETL finds plans with outputs that are 25 to 80% more accurate than well-engineered baselines, addressing a critical gap in unstructured data analysis. DocETL is open-source at docetl.org, and as of March 2025, has amassed over 1.7k GitHub Stars, with users spanning a variety of domains.