Inclusion Criteria:  NYHA Class II at screening with a prior history of greater than NYHA Class II, OR NYHA Class III at screening, OR ambulatory Class IV at screening: with documented medical history of heart failure for at least 6 months prior to the screening visit. Medical history within the past 12 months of at least one hospitalization with heart failure as the primary or secondary diagnosis OR treatment with IV diuretics for heart failure. Calculated LVEF (by Echo) ≤ 40% as measured by the study-specific transthoracic echocardiography. Elevated left atrial pressure WITH a gradient compared to right atrial pressure (RAP) documented by: (1) end-expiratory PCWP at peak supine cycle ergometer exercise ≥ 25mmHg AND (2) PCWP greater than RAP by ≥ 5 mmHg, OR (1) ≥ 10 mmHg increase of end-expiratory PCWP at peak supine cycle ergometer exercise compared to resting PCWP AND (2) PCWP greater than RAP by ≥ 5 mmHg. Patients must also have PCWP greater than RAP by ≥ 5 mmHg at rest.  Exclusion Criteria:  Presence of advanced heart failure documented in the medical history, defined as one or more of the following:  ACC/AHA/ESC Stage D heart failure, non-ambulatory NYHA Class IV HF. Cardiac index <1.5 L/min/m2. Patient is on the cardiac transplant waiting list. CIP-0004 Rev 01 - ALLEVIATE-HFrEF Study Confidential Alleviant Medical, Inc. Page 9 of 64 Inotropic infusion (continuous or intermittent) for EF < 40% within the past 6 months. History of mechanical cardiac support within 6 months.  Presence of moderate or worse uncorrected valve disease documented in the medical history and/or confirmed by the study-specific transthoracic echocardiography protocol performed during screening, defined as one or more of the following:  Moderate or worse degenerative mitral valve regurgitation or moderate or worse mitral stenosis. Severe functional mitral regurgitation. Moderate or worse tricuspid valve regurgitation. Moderate or worse aortic valve disease defined as moderate or worse aortic stenosis. Severe aortic regurgitation. Presence of clinically significant untreated carotid artery stenosis documented in the medical history that is likely to require intervention. Presence of clinically significant un-revascularized coronary artery disease documented in the medical history that is likely to require intervention, defined as epicardial coronary artery stenosis associated with frequent angina not well controlled with medical therapy or other evidence of coronary ischemia. Presence of infiltrative or hypertrophic cardiomyopathy documented in the medical history. Presence of uncontrolled tachyarrhythmia documented in the medical history.  Medical history ofone or more of the following cardiac procedures:  MI and/or percutaneous coronary intervention (PCI) within the past 3 months; CABG within the past 3 months; SAVR or TAVR within the past 6 months; MVR or TMVR within the past 6 months; Medical history of cardiac resynchronization therapy within the past 6 months or any implanted pacemaker device (or leads) placed within the past 6 months. Medical history of lead revision or ablation procedure (either for atrial or ventricular arrhythmias) within the past 3 months.  Presence of chronic pulmonary disease documented in the medical history, defined by one or more of the following:  Current requirement for continuous home oxygen use. Hospitalization within the past 12 months for treatment of chronic pulmonary disease. Significant chronic pulmonary disease defined as FEV1 < 50%. Presence of pulmonary hypertension with PASP ≥ 70 mmHg OR PVR > 4 Wood units, documented in the medical history.