Medical technologies can target care to patients identified through screening, raising questions of how broadly to screen for potential use. We explore this empirically in the context of a non-invasive prenatal screening, cfDNA, which is used to target a more costly invasive test that elevates miscarriage risk. Using Swedish administrative data on prenatal choices for pregnancies conceived between 2011 and 2019 { a period in which Swedish regions began providing coverage for the new screening { we document that coverage of cfDNA substantially increases cfDNA screening and reduces invasive testing. To assess the impact of counterfactual targeting of cfDNA coverage, we develop and estimate a stylized model of prenatal choices. We find that narrow targeting of cfDNA coverage can improve outcomes and reduce costs, while broader coverage also improves outcomes but with increased costs. These findings point to the potential gains from well-designed targeting of screening, but at the same time highlight the importance of the targeting design.