In transverse-jet systems, a main jet is introduced into a cross-flowing stream. The high shear-rate induced by this flow configuration should theoretically enhance jet mixing, allowing the use of shorter reactors. However, such jets are highly sensitive to the operating conditions including the level of turbulence and the ratio of the velocities of the two streams. It has been found that the formation and breakdown of coherent vortical structures determine mixing efficiency. The jet operating conditions significantly alter the strength and location of these structures, thereby changing the mixing characteristics. One key issue that is often not discussed is the role that the main jet inlet shape plays in the organization of these flow structures. In this regard, out objective is to understand if enhanced jet mixing can be achieved through geometric optimization. For this purpose, we performed direct numerical simulation of transverse jets at Reynolds number of 3000 based on the main jet properties. Several different inlet shapes including rectangular, ellipsoidal, and triangular geometries were considered. The computational grid consisted of nearly 30 million control volumes that ensured that the smallest turbulent length-scales were resolved. For comparison purpose, the ratio of the cross-flow to the main-jet mass flow rate was set to be equal for all cases. It was found that the jet exit shape altered the near-field mixing characteristics. Vortex sheets formed in the jet shear-layers were found to evolve differently for the different exit shapes. Spanwise-averaged passive-scalar root-mean square fluctuations was used as a measure of mixing rate. It was found that the effect of the inlet shape was mainly limited to the near-field region. Further downstream, as the cross-flow jet evolves into a fully-developed turbulent flow, the mixing rates were almost identical. Further analyses of this complex flow-field provided some interesting insights that can be used for increasing the jet efficiency.