Chebyshev center-based column generation, CCG, is a gently stabilized variant of classical column generation, CG, that relies on dual information provided by central interior points to identify new improving columns [3]. From a dual perspective, the basic algorithm corresponds to the well-known Chebyshev center cutting plane method, which draws on weak dual bounds and converges still rather slow in practice [1, 3]. We present deep Chebyshev center-based column generation, DCCG, a sophistication operating on stronger bounds and employing deeper cuts. Besides giving first numerical evidence of its superiority over both classical and state-of-the-art Chebyshev center-based column generation, we provide interesting analytical insights that lay the foundation for further improvements in the realm of column generation and beyond.