Existing deep-search agents use a Search-Visit workflow that retrieves whole webpages without considering the structure they expose through titles, headings, sections, and metadata. This prevents agents from directly constraining retrieval to parts of a webpage and often carries irrelevant content into their context. We introduce Sieve, a search-inspect-fetch strategy driven by a Boolean Query Language (BQL): it searches webpage fields to filter candidates, uses an interchangeable ranker to order them, presents structure-rich result cards for inspection, and fetches only selected sections. Across three QA collections, Sieve is more accurate than the strongest conventional Search-Visit configuration on each collection while using 20.7-50.6% fewer tokens. Boolean filtering improves every tested ranker, and the accuracy-context advantage persists across retriever choices and agent backbones. Our implementation is included in the SkimSearchAgent library https://github.com/ielab/skim-search-agent.

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