The data from previous studies suggest that doses of NATRECOR® hBNP may be a potent agent for the treatment of acute congestive heart failure (CHF) with a unique combination of desirable effects on the flow of blood throughout the body; the hormones secreted by the nervous system and support of copious salt outputs by the renal system not provided by currently available therapies. This study is a multicenter, open-label pilot study in which subjects who have received treatment for acutely decompensated CHF during a hospitalization at least twice within the previous 12 months are randomized (1:1:1) to one of three treatment groups. One treatment group will receive their usual long term cardiac medications, either with or without serial infusions of inotropes (various drugs that affect the strength of contractions of the heart muscle) and without nesiritide therapy. The 0.005 mcg/kg/min nesiritide treatment group receives a 0.5 mcg/kg bolus of nesiritide followed by a 0.0025 mcg/kg/min infusion, in addition to their usual long term cardiac medications, excluding IV inotropes; The 0.010 mcg/kg/min nesiritide treatment group receives a 1 mcg/kg bolus of nesiritide followed by a 0.005 mcg/kg infusion, in addition to their usual long term cardiac medications, excluding IV inotropes. Because patients treated in an outpatient setting may be less decompensated than patients with acutely decompensated heart failure, this study was designed to evaluate the 0.010 mcg/kg/min dose of nesiritide (the currently approved dose for acutely decompensated patients) as well as a lower dose (0.005 mcg/kg/min).