Users typically interact with a database by asking queries and examining the results. We refer to the user examining the query results and asking follow-up questions as query result exploration. Our work builds on two decades of provenance research useful for query result exploration. Three approaches for computing provenance have been described in the literature: lazy, eager, and hybrid. We investigate lazy and eager approaches that utilize constraints that we have identified in the context of query result exploration, as well as novel hybrid approaches. For the TPC-H benchmark, these constraints are applicable to 19 out of the 22 queries, and result in a better performance for all queries that have a join. Furthermore, the performance benefits from our approaches are significant, sometimes several orders of magnitude.