This chapter is a continuation of [PR2, Chap. 3 ] on the lattice of varieties of bands. It grows out of the fact that the mapping of each \(\mathcal {V} \in \mathcal {L}(\mathcal{C}\mathcal{R})\) to its intersection with the variety of bands \(\mathcal {B}\) is a complete retraction of \(\mathcal {L}(\mathcal{C}\mathcal{R})\) to \(\mathcal {L}(\mathcal {B})\) and therefore induces a complete congruence \(\textbf{B}\) on \(\mathcal {L}(\mathcal{C}\mathcal{R})\) whose classes are all intervals.