This work presents a new data-driven progressive compression method of colored 3D meshes. The proposed method improves the visual quality of the progressive compression by using texture mapping. Additionally, a cubic cell complex is computed to drive the compression process in order to allow the intermediate meshes to share a common colored texture. The experimental results show that our approach based on color textures improves the visual quality of low resolution intermediate meshes as compared to traditional methods based on color per vertex. The method is well suited for remote visualization scenarios where the visual appearance is as important as the compact representation of 3D meshes.