We provide insights into the design and understanding of thermal rectifiers based on asymmetric MoS2 nanoribbons. Non-equilibrium molecular dynamics (NEMD) simulations are used to study the influence of geometrical shapes on the thermal rectification. Our results point out that asymmetric MoS2 nanoribbons can display considerable thermal rectification. Moreover, this rectifier effect increases with the asymmetry degree of the device but, as expected, it weakens with increasing linear dimensions. Among the geometrical shapes studied in the present work, T-shaped MoS2 nanoribbons present the highest thermal rectification for each asymmetry degree. We also found that vibrational modes for frequencies greater than 380 cm-1 are almost fully localized and spatially distributed on the edges of the asymmetric nanoribbons. Thus, similar to asymmetric and defective nanostructures made of a single material, we find that lateral confinement of the vibrational modes is a mechanism of thermal rectification in MoS2 nanoribbons.