Branching bisimilarity is a well-known equivalence relation for labelled transition systems. Based on this equivalence relation, with an additional simple rootedness condition, a congruence relation for calculus of communication system (CCS) processes can be obtained. However, neither branching bisimilarity nor the corresponding congruence relation preserves divergence, and it is still a question whether, based on a divergence-preserving variant of branching bisimilarity, a divergence-preserving congruence relation for CCS processes can be obtained by introducing the same simple rootedness condition. In this article, we present a partial solution by showing that rooted divergence-preserving branching bisimilarity is preserved under the usual CCS operators, including prefixing, summation, parallel composition, relabelling, restriction, and (weakly) guarded recursion.