Reducing the residence time of drops on solids has been attracting much attention in a wide range of industrial methods, such as self-cleaning and anti-icing. Classical drop dynamics is generally confined to circular symmetry and a theoretical limit of the bouncing time. In this study, we investigate the bouncing dynamics of ellipsoidal drops on cylindrical surfaces. Experimental and numerical results show that, compared with spherical ones, ellipsoidal shapes create the synergy effect of a preferential flow along the curved side, thereby leading to a significant reduction in the residence time when the drop's major axis coincides with the cylinder's axial direction. The effects of the drop ellipticity and surface curvature on the bouncing dynamics are investigated for several Weber numbers and discussed through momentum analyses. The proposed concave/convex decorated models demonstrate the feasibility of the further reduced residence time by enhancing the asymmetry in the mass and momentum distributions. This study can provide a new perspective to shape-dependent impact dynamics by emphasizing the importance of the geometric configuration between ellipsoidal drops and anisotropic surfaces in determining the extent to which the dynamics are asymmetric.