Pitch plays a crucial role in speech and music, but is highly degraded for people with cochlear implants, leading to severe communication challenges in noisy environments. Pitch is determined primarily by the first few spectrally resolved harmonics of a tone. In implants, access to this pitch is limited by poor spectral resolution, due to the limited number of channels and interactions between adjacent channels. Here we used noise-vocoder simulations to explore how many channels, and how little channel interaction, are required to elicit pitch. Results suggest that two to four times the number of channels are needed, along with interactions reduced by an order of magnitude, than available in current devices. These new constraints not only provide insights into the basic mechanisms of pitch coding in normal hearing but also suggest that spectrally based complex pitch is unlikely to be generated in implant users without significant changes in the method or site of stimulation.