Dynamic element matching (DEM) has been widely researched in the domain of digital-to-analog converters. Different architectures, noise shapes and ever higher order shaping have been devised. However, beyond first order, no schemes guarantee the absence of tones. Herein presents a band-pass shaping scheme that is provably toneless based on tree structured DEM. This scheme does incur a noise penalty and additional hardware. However, the former of which can be controlled and the later of which is only moderate.