Background: Heart failure with preserved ejection fraction (HFPEF) is a common, globally recognised, form of heart failure for which no treatment has yet been shown to improve symptoms or prognosis. The pathophysiology of HFPEF is complex but characterised by increased left atrial pressure, especially during exertion, which might be a key therapeutic target. The rationale for the present study was that a mechanical approach to reducing left atrial pressure might be effective in HFPEF. Methods: The REDUCe Elevated Left Atrial Pressure in Patients with Heart Failure (REDUCE LAP-HF) study was an open-label, single-arm, phase 1 study designed to assess the performance and safety of a transcatheter interatrial shunt device (IASD, Corvia Medical, Tewkesbury, MA, USA) in patients older than 40 years of age with symptoms of HFPEF despite pharmacological therapy, left ventricular ejection fraction higher than 40%, and a raised pulmonary capillary wedge pressure at rest (>15 mm Hg) or during exercise (>25 mm Hg). The study was done at 21 centres (all departments of cardiology in the UK, Netherlands, Belgium, France, Germany, Austria, Denmark, Australia, and New Zealand). The co-primary endpoints were the safety and performance of the IASD at 6 months, together with measures of clinical efficacy, including functional capacity and clinical status, analysed per protocol. This study is registered with ClinicalTrials.gov, number NCT01913613. Findings: Between Feb 8, 2014, and June 10, 2015, 68 eligible patients were entered into the study. IASD placement was successful in 64 patients and seemed to be safe and well tolerated; no patient had a peri-procedural or major adverse cardiac or cerebrovascular event or need for cardiac surgical intervention for device-related complications during 6 months of follow-up. At 6 months, 31 (52%) of 60 patients had a reduction in pulmonary capillary wedge pressure at rest, 34 (58%) of 59 had a lower pulmonary capillary wedge pressure during exertion, and 23 (39%) of 59 fulfilled both these criteria. Mean exercise pulmonary capillary wedge pressure was lower at 6 months than at baseline, both at 20 watts workload (mean 32 mm Hg [SD 8] at baseline vs 29 mm Hg [9] at 6 months, p=0·0124) and at peak exercise (34 mm Hg [8] vs 32 [8], p=0·0255), despite increased mean exercise duration (baseline vs 6 months: 7·3 min [SD 3·1] vs 8·2 min [3·4], p=0·03). Sustained device patency at 6 months was confirmed by left-to-right shunting (pulmonary/systemic flow ratio: 1·06 [SD 0·32] at baseline vs 1·27 [0·20] at 6 months, p=0·0004). Interpretation: Implantation of an interatrial shunt device is feasible, seems to be safe, reduces left atrial pressure during exercise, and could be a new strategy for the management of HFPEF. The effectiveness of IASD compared with existing treatment for patients with HFPEF requires validation in a randomised controlled trial.