Supporting one-handed thumb operation of touchscreen-based mobile devices presents a challenging tradeoff between visual expressivity and ease of interaction. ThumbSpace and Shift—two new application-independent, software-based interaction techniques—address this tradeoff in significantly different ways; ThumbSpace addresses distant objects while Shift addresses small object occlusion. We present two extensive, comparative user studies. The first compares ThumbSpace and Shift to peripheral hardware (directional pad and scrollwheel) and direct touchscreen input for selecting objects while standing and walking. The data favored the Shift design overall, but suggested ThumbSpace is promising for distant objects. Our second study examines the benefits and learnability of combining Shift and ThumbSpace on a device with a larger screen (3.5"). We found their combined use offered users better overall speed and accuracy in hitting small targets (3.6 mm) than using either method alone.