Current touch-based UIs commonly employ regions near the corners and/or edges of the display to accommodate essential functions. As the screen size of mobile phones is ever increasing, such regions become relatively distant from the thumb and hard to reach for single-handed use. In this paper, we present two techniques: CornerSpace and BezelSpace, designed to accommodate quick access to screen targets outside the thumb's normal interactive range. Our techniques automatically determine the thumb's physical comfort zone and only require minimal thumb movement to reach distant targets on the edge of the screen. A controlled experiment shows that BezelSpace is significantly faster and more accurate. Moreover, both techniques are application-independent, and instantly accommodate either hand, left or right.