[en] Recoil atoms detected in Elastic Recoil Detection (ERD) experiments emerge from an initial collision area along cones of constant energy due to the cylindrical symmetry of the elastic scattering cross section. The constant energy cones therefore intercept planar slit plates placed before the detectors in conic sections. For ease of fabrication slits are typically configured as long narrow rectangles, and as a result energy resolution is adversely affected. It has been shown that the kinematic broadening caused by using rectangular slits is minimized when L = 2 (W z tanΘ_recoil)^1/2 where W is the slit width, L is the slit length, z is the slit-target distance and Θ_recoil is the lab-frame recoil angle. The improved energy resolution which results when rectangular slits are replaced by appropriate curved slits is examined here. Formulas are given for the conic sections associated with the curved slits as a function of experimental geometry. When slit dimensions are small compared with the full extent of the conic section slit geometry can be accurately approximated as the arc of a circle with radius R_c = z tanΘ_recoil. Energy loss effects on the resolution are also accounted for in our treatment. The use of curved slits with L = 4 (W z tanΘ_recoil)^1/2 is shown to improve kinematic broadening by ∼50% as compared to optimized rectangular slits of the same area. 2 refs., 5 figs