We have used Monte Carlo simulations to investigate the magnetic properties of asymmetric dots as a function of their geometry. The asymmetry of round dots is produced by cutting off a fraction of the dot and is characterized by an asymmetry parameter α. This shape asymmetry has interesting effects on the coercivity (Hc), remanence (Mr), and barrier for vortex and C-state formation. The dependences of Hc and Mr are nonmonotonic as a function of α with a well defined minima in these parameters. The vortex enters the most asymmetric part and exits through the symmetric portion of the dot. With increasing α the vortex formation starts with a C-state which persists for longer fields and the barrier for vortex exit diminishes with increasing asymmetry, thus providing control over the magnetic chirality. This implies interesting, naively unexpected, magnetic behavior as a function of geometry and magnetic field.