Strong effects of modulated demagnetizing fields on the attenuation of Hahn echoes in liquids are shown theoretically as well as experimentally. As such demagnetizing fields are the basis of non-linear evolution leading to multiple echoes, it follows that the dominating nature of such echo signals is of a purely single-quantum character. It is concluded that the contribution of intermolecular multiple-quantum coherence transfer echoes to the multiple echoes is negligible. The effects shown in this study are of major impact for NMR spectroscopy with high-field instruments as they nowadays are in ubiquitous use.