Signal inhomogeneities in MRI often appear as multiplicative weightings due to various factors such as field-inhomogeneity dependencies for steady-state free precession (SSFP) imaging or receiver sensitivities for coil arrays. These signal inhomogeneities can be reduced by combining multiple data sets with different weights. A sum-of-squares combination is typically used due to its simplicity and near-optimal signal-to-noise ratio (SNR). However, this combination may lead to residual signal inhomogeneity. Alternatively, an optimal linear combination of the data can be performed if the weightings for individual data sets are estimated accurately. We propose a nonlinear combination to improve image-based estimates of the individual weightings. The signal homogeneity can be significantly increased without compromising SNR. The improved performance of the method is demonstrated for SSFP banding artifact reduction and multicoil (phased-array and parallel) image reconstructions.