Data provenance is essential for debugging query results, auditing data in cloud environments, and explaining outputs of Big Data analytics. A well-established technique is to represent provenance as annotations on data and to instrument queries to propagate these annotations to produce results annotated with provenance. However, even sophisticated optimizers are often incapable of producing efficient execution plans for instrumented queries, because of their inherent complexity and unusual structure. Thus, while instrumentation enables provenance support for databases without requiring any modification to the DBMS, the performance of this approach is far from optimal. In this work, we develop provenance specific optimizations to address this problem. Specifically, we introduce algebraic equivalences targeted at instrumented queries and discuss alternative, equivalent ways of instrumenting a query for provenance capture. Furthermore, we present an extensible heuristic and cost-based optimization (CBO) framework that governs the application of these optimizations and implement this framework in our GProM provenance system. Our CBO is agnostic to the plan space shape, uses a DBMS for cost estimation, and enables retrofitting of optimization choices into existing code by adding a few LOC. Our experiments confirm that these optimizations are highly effective, often improving performance by several orders of magnitude for diverse provenance tasks.