This paper investigates thumb-index interaction on touch input devices, and more precisely the potential of two concurrent stroke gestures, i.e. gestures in which two fingers of the same hand concurrently draw one stroke each. We present two fundamental studies, one using such gestures for two-dimensional control, by precisely drawing figures, and the other for command activation, by roughly sketching figures. Results give a first analysis of user performance on 35 gestures with a varying complexity based on numbers of turns and symmetries. All 35 gestures, were grouped into six families. From these results we classify these families and propose new guidelines for designing future mobile interfaces. For instance, favoring anchored gestures (forefinger drawing while the thumb remains still on the surface) to increase input bandwidth when forefinger precision is required.