This paper presents a method to grasp objects that cannot be picked directly from a table, using a soft, underactuated hand. These grasps are achieved by dragging the object to the edge of a table, and grasping it from the protruding part, performing so-called slide-to-edge grasps. This type of approach, which uses the environment to facilitate the grasp, is named Environmental Constraint Exploitation (ECE), and has been shown to improve the robustness of grasps while reducing the planning effort. The paper proposes two strategies, namely Continuous Slide and Grasp and Pivot and Re-Grasp, that are designed to deal with different objects. In the first strategy, the hand is positioned over the object and assumed to stick to it during the sliding until the edge, where the fingers wrap around the object and pick it up. In the second strategy, instead, the sliding motion is performed using pivoting, and thus the object is allowed to rotate with respect to the hand that drags it toward the edge. Then, as soon as the object reaches the desired position, the hand detaches from the object and moves to grasp the object from the side. In both strategies, the hand positioning for grasping the object is implemented using a recently proposed functional model for soft hands, the closure signature, whereas the sliding motion on the table is executed by using a hybrid force-velocity controller. We conducted 320 grasping trials with 16 different objects using a soft hand attached to a collaborative robot arm. Experiments showed that the Continuous Slide and Grasp is more suitable for small objects (e.g., a credit card), whereas the Pivot and Re-Grasp performs better with larger objects (e.g., a big book). The gathered data were used to train a classifier that selects the most suitable strategy to use, according to the object size and weight. Implementing ECE strategies with soft hands is a first step toward their use in real-world scenarios, where the environment should be seen more as a help than as a hindrance.