True amplitude inversion is often carried out without taking into account migration distortions to the wavelet. Seismic migration leaves a dip-dependent effect on the wavelet that can cause significant inaccuracies in the inverted impedances obtained from conventional inversion approaches based on 1D vertical convolutional modeling. Neglecting this effect causes misleading inversion results and leakage of dipping noise and migration artifacts from the higher frequency bands to the lower frequencies. I have observed that, despite the dip dependency of this effect, low-dip and flat events may also suffer if they are contaminated with cross-cutting noise, steep migration artifacts, and smiles. I adopt an efficient, effective, and reversible data preconditioning approach that accounts for the dip dependency of the wavelet and is applied to migrated images prior to inversion. My proposed method consists of integrating data with respect to the total wavenumber followed by the differentiation with respect to the vertical wavenumber. This process is equivalent to applying a deterministic dip-consistent preconditioning that projects the data from the total wavenumber to the vertical wavenumber axis. This preconditioning can be applied to pre- and poststack data as well as to amplitude-variation-with-offset attributes such as intercept and gradient before inversion. The vertical image projection methodology that I adopt here reduces the impact of migration artifacts such as cross-cutting noise and migration smiles and improves inverted impedances in synthetic and real data examples. In particular, I indicate that neglecting the proposed preconditioning leads to anomalously higher impedance values along the steeply dipping structures.