In this work, we discuss the design of soft robotic fingers for robust precision grasping. Through a conceptual analysis of the finger shape and compliance during grasping, we confirm that antipodal grasps are more stable when contact with the object occurs on the side of the fingers (i.e., pinch grasps) instead of the fingertips. In addition, we show that achieving such pinch grasps with soft fingers for a wide variety of objects requires at least two independent bending segments each, but only requires actuation in the proximal segment. Using a physical prototype hand, we evaluate the improvement in pinch-grasping performance of this two-segment proximally actuated finger design compared to more typical, uniformly actuated fingers. Through an exploration of the relative lengths of the two finger segments, we show the tradeoff between power grasping strength and precision grasping capabilities for fingers with passive distal segments. We characterize grasping on the basis of the acquisition region, object sizes, rotational stability, and robustness to external forces. Based on these metrics, we confirm that higher-quality precision grasping is achieved through pinch grasping via fingers with the proximally actuated finger design compared to uniformly actuated fingers. However, power grasping is still best performed with uniformly actuated fingers. Accordingly, soft continuum fingers should be designed to have at least two independently actuated serial segments, since such fingers can maximize grasping performance during both power and precision grasps through controlled adaptation between uniform and proximally actuated finger structures.