We present results on coherent control of ultracold trap-loss collisions using 40-ns pulses of nonlinearly frequency-chirped light. The chirps, either positive or negative, sweep ∼1 GHz in 100 ns and are centered at various detunings below the D 2 line of 85 Rb. At each center detuning, we compare the collisional rate constant β for chirps that are linear in time, concave-down, and concave-up. For positive chirps, we find that β generally depends very little on the shape of the chirp. For negative chirps, however, we find that β can be enhanced by up to 50(20)% for the case of the concave-down shape. This occurs at detunings where the evolution of the wave packet is expected to be coherent. An enhancement at these detunings is also seen in quantum-mechanical simulations of the collisional process.