Broadcast is a fundamental operation in wireless ad hoc networks (WANETs). To design efficient broadcast protocols, one of the most important concerns is to reduce broadcast redundancy. In conventional WANETs where nodes are always active, due to the broadcast nature of wireless medium, minimizing broadcast redundancy is equivalent to finding a Minimum Connected Dominating Set (MCDS). However, this is not true for uncoordinated duty-cycled WANETs, where each node periodically switches between active and sleep states, and can only hear messages when it is active. In this paper, we investigate the minimum redundancy broadcast problem in uncoordinated duty-cycled WANETs. We first show that by modifying the conventional CDS-based approaches properly, a constant-approximation broadcast algorithm (MCA) can be obtained. We then propose a hierarchical CDS-based algorithm (HCA), improving the best known approximation ratio from 20 to 13.67. Both algorithms are distributed, and with low time and message complexities. Simulation results show that our algorithms achieve about 5%-30% performance improvement over the state-of-the art scheme.