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In this paper, we study the problem of constructing quality fault-tolerant Connected Dominating Sets (CDSs)in homogeneous wireless networks, which can be defined as minimum k-Connected m-Dominating Set ((k;m)-CDS) problem in Unit Disk Graphs (UDGs). We found that every existing approximation algorithm for this problem is incomplete for k >= 3 in a sense that it does not generate a feasible solution in some UDGs. Based on these observations, we propose a new polynomial time approximation algorithm for computing (3;m)-CDSs. We also show that our algorithm is correct and its approximation ratio is a constant.