Recent experiments (M'Closkey et al. 2002, Shapiro et al. 2006, Johari 200C, Eroglu and Briedenthal 2001) on pulsed jets in crossflow show that jot penetration and spread can be optimized at specific pulse conditions. We perform DNS to study the evolution and mixing behavior of jets in crossflow at different velocity ratios with fully modulated square wave excitation. We attempt to explain the wide range of optimal pulsing conditions found in different experiments by noting that pulsing generates vortex rings. Sau and Mahesh (J. Fluid Mech., 2008) show that vortex rings in crossflow exhibit three distinct flow regimes depending on stroke ratio and ring velocity ratio. We use the behavior of a single vortex ring in crossflow to explain the evolution of pulsed jets in crossflow. Simulations suggest that the optimal conditions can be predicted from the transition behavior of vortex rings between different regimes. A11 optimal map in stroke ratio and velocity ratio space is presented and used to obtain an a-priori estimate of optimal conditions. Good comparison with different experimental optimal conditions are obtained in terms of stroke ratio and ring velocity ratio.