Given a Boolean function, the Unate-Covering Problem (UCP) is NP-hard. This problem can be modeled as a setcover problem where minterms are the elements and implicants form the sets. Traditional solutions in logic synthesis use setcover algorithms that are oblivious to the special semantic of the elements and sets. We propose three new heuristics for the set-cover problem which are aware of the relationship between implicants and minterms. We show that the proposed heuristics are effective for breaking ties when a cyclic core is obtained. We evaluate the heuristics on a set of hard instances from BHOSLIB benchmark suite. We also replace ESPRESSO's set cover algorithm using these heuristics and compare the logic synthesis results. We further map the minimized Boolean equations using ABC's technology mapping tool using 2-input NAND gates and 4-input Lookup Tables (LUTs). © 2012 IEEE.