We investigate the characteristics of the oscillatory motion and wake of confined bubbles freely rising in a thin-gap cell (h=3.1 mm width). Once the diameter d of the bubble in the plane of the cell is known, the mean vertical velocity of the bubble Vb is proportional to the gravitational velocity [...], where g is the gravitational acceleration. This velocity is used to build the Reynolds number [...] that characterizes the flow induced by the bubble in the surrounding liquid (of kinematic viscosity ν), and which determines at leading order the mean deformation of the bubble given by the aspect ratio χ of the ellipse equivalent to the bubble contour. We then show that in the reference frame associated with the bubble (having a fixed origin and axes corresponding to the minor and major axes of the equivalent ellipse) the characteristics of its oscillatory motion in the plane of the cell display remarkable properties in the range 1200