We simulated the effect of several automatic gain control (AGC) and AGC-like systems and head movement on the output levels, and resulting interaural level differences (ILDs) produced by bilateral cochlear-implant (CI) processors. The simulated AGC systems included unlinked AGCs with a range of parameter settings, linked AGCs, and two proprietary multi-channel systems used in contemporary CIs. The results show that over the range of values used clinically, the parameters that most strongly affect dynamic ILDs are the release time and compression ratio. Linking AGCs preserves ILDs at the expense of monaural level changes and, possibly, comfortable listening level. Multichannel AGCs can whiten output spectra, and/or distort the dynamic changes in ILD that occur during and after head movement. We propose that an unlinked compressor with a ratio of approximately 3:1 and a release time of 300-500 ms can preserve the shape of dynamic ILDs, without causing large spectral distortions or sacrificing listening comfort.