The Digital Delta-Sigma Modulator (DDSM) has the disadvantage of presenting a periodic output for constant inputs, affecting the benefits of noise-shaping modulation. This work uses the linearized model to expose the principal features of the recent solutions. The analysis results in two ideas: the first is a mix of the Song-and-Park Multi-stAge-noise-SHaping (SP-MASH topology) with the appropriate dither elimination, another option is a MASH modified by applying an XOR based dither to the input of the second accumulator. The work validates the proposed solutions with the mathematical, the spectral, and the hardware synthesis showing the benefit of the proposed schemes with the output spectrum using a 9-bit implementation for each case. The results show the idle tones do not appear for all the possible input values. The hardware increase is 3 percent compared to the third order dithered input SP MASH solution.