A pulsed welding regime includes a peak phase in which energy is added to an electrode and a weld puddle, and a molten ball begins to detach from the electrode, followed by a dabbing phase in which current is significantly reduced to place the ball in the weld puddle with addition of little or no energy. The resulting short circuit clears and the system proceeds to a background phase. The current in the dabbing phase is lower than the current during the background phase. The process may be specifically adapted for particular welding wires, and may be particularly well suited for use with cored wires. The dabbing phase allows for lower energy to be transferred to the sheath of such wires, and resets the arc length after each pulse cycle.