This paper examines the efficiency of a simple distributed algorithm, called Round-2, for further decreasing the size of connected dominating set (CDS) in ad hoc networks and evaluates its performance based on neighbors-covered and neighbor-pair-connected algorithms under two categories of local static priority information: node-identifier-based and node-degree-based. The Round-2 algorithm decreases the size of CDS by fixing half forward nodes determined in the first round and re-evaluating the other half nodes. The neighbors-covered algorithms decrease the size of CDS by checking whether neighbors of a node are covered by intermediate nodes with higher priority than that node. The neighbor-pair-connected algorithms do it by checking whether two neighbors of a node are connected via intermediate nodes with higher priority. The performance of the Round-2 algorithm with different numbers of non-restricted intermediate nodes is simulated.