The ability to obtain high-quality images of small structures, such as the nerves of the inner ear, is important for the early diagnosis of numerous conditions. Balanced steady-state free precession (SSFP; e.g., true fast imaging with steady-state precession) is a fast acquisition method, but its use has been limited by the presence of off-resonance banding artifacts. To reduce these artifacts multiacquisition balanced SSFP with phase cycling is used, yielding multiple data sets in which the banding artifacts are spatially shifted with respect to each other (e.g., as in CISS). We present a new method, called nonlinear averaging (NLA), for combining these data sets to reduce banding artifacts. The NLA method arithmetically averages the three highest magnitude signals from four-phase-cycle SSFP data on a pixel-by-pixel basis. Simulations indicate that NLA offers improved signal-to-noise ratio (SNR) over the more standard maximum intensity projection (MIP) reconstruction. NLA is compared to MIP in simulations and volunteer tests. Simulations suggest that NLA provides substantially improved SNR compared to MIP. In a randomized blinded comparison of 10 volunteer studies, two radiologists found that NLA, compared to MIP, gave improved results. NLA also provided superior noise reduction and enhanced edge sharpness compared to MIP. We demonstrate that NLA, similar to MIP, improves SNR and image quality. It does so consistently in all situations to which it is applied.