Abstract: Disclosed is a catheter having an elongated cannula with an infusion lumen and a pressure-sensing lumen, and a portion of the cannula which tapers to form a distal end which is narrower than the more proximal portions of the cannula. The distal end of the cannula has a rounded tip and forms at least one infusion lumen opening and a pressure-sensing opening. A balloon is attached to and surrounds the cannula near the distal end while being in fluid communication with the infusion lumen through one or more inflation openings. The infusion lumen openings are smaller than the inflation openings so as to make the balloon self-inflating. Also disclosed is a method for using such a catheter to perform cardioplegia by the retrograde infusion of a cardioplegic fluid into the coronary sinus.