A positionable, direct-injection catheter that can access a specific region of the heart or other organ. The catheter is provided with one or two needle shafts, which may be located within respective sheaths that extend axially along the interior of the lumen of a main catheter shaft. Each needle shaft carries, at a distal end thereof a penetrable element or “needle” that is normally retracted within the distal tip of the main shaft during travel to the target organ, but is subsequently deployed by action of a handle-mounted trigger mechanism to extend the needles into the organs wall. Each extended needle is curved to relative to the shafts axis to enter the organ wall in a flattened trajectory that both reduces the chance of puncture through the wall and anchors the needles into the wall during injection (for reduced chance of pullout under pressure). A plurality of apertures which provide for more complete agent delivery rapidly, while maintaining a low delivery velocity to effect treatment delivery in as short a period of time as possible without the problems caused by high velocity delivery. The needles are typically arranged to exit the tip at contralateral orientations relative to each other.