The impact of joint partial-time, partial-band jamming on a multicarrier (MC) asynchronous direct-sequence code-division multiple access (DS-CDMA) system in a fast fading environment is studied in conjunction with two different subcarrier combining and decoding schemes. An easy-to-evaluate upper bound using the Chernoff bound is provided and compared to simulation results. Simulation results suggest that for soft-decision decoding systems, under Rayleigh fading, full-time, full-band jamming is most effective. In contrast to the Rayleigh case, when a sufficiently strong line-of-sight component exists in the channel, the jammer's optimal strategy of attacking in time or frequency depends on the strength and the type of error correction that the system is deploying for that dimension. For hard-decision decoding systems, in Rayleigh fading, partial-band jamming is recommended. For the coding strategies examined, in Rician fading, the jammer should switch from full-time, partial-band jamming to a strategy that jams a higher percentage of the more heavily protected dimension as the jamming power increases. Furthermore, for AWGN channels, the results from the system show that the jammer should always jam a higher percentage of the more heavily protected dimension.