We reexamine a 50+ yr old problem of deep central reversals predicted for strong solar spectral lines, in contrast to the smaller reversals seen in observations. We examine data and calculations for the resonance lines of H I, Mg II, and Ca II, the self-reversed cores of which form in the upper chromosphere. Based on 3D simulations, as well as data for the Mg II lines from the Interface Region Imaging Spectrograph (IRIS), we argue that the resolution lies not in velocity fields on scales in either of the micro- or macroturbulent limits. Macroturbulence is ruled out using observations of optically thin lines formed in the upper chromosphere, and by showing that it would need to have unreasonably special properties to account for critical observations of the Mg II resonance lines from the IRIS mission. The power in "turbulence" in the upper chromosphere may therefore be substantially lower than earlier analyses have inferred. Instead, in 3D calculations horizontal radiative transfer produces smoother source functions, smoothing out intensity gradients in wavelength and in space. These effects increase in stronger lines. Our work will have consequences for understanding the onset of the transition region, for understanding the energy in motions available for heating the corona, and for the interpretation of polarization data in terms of the Hanle effect applied to resonance line profiles.