A fault f_j is said to dominate another fault f_i if all tests for f_i detect f_j. When two faults dominate each other, they are called equivalent. Dominance and equivalence relations among faults around a Boolean gate are called "structural" and are used for fault collapsing in large circuits. Some fault equivalences, that cannot be determined by the structural analysis, can be found by "functional" equivalence relations. This paper gives a "functional dominance" relation, which has not been described in the literature. Since the functional analysis is computationally expensive, it can only be applied to small circuits such as standard cells. A graph-theoretic hierarchical fault collapsing method from the recent literature can then collapse faults in any large cell-based circuit. It is found that the size of the dominance collapsed set for an exclusive-OR cell reduces to just four faults when functional dominance is considered. With the traditional method of structural collapsing this set contains 13 faults. When the exclusive-OR cell is used to build an 8-bit adder circuit, the size of the dominance collapsed set reduces to 112 faults from a total of 466 faults. Traditional structural dominance collapsing would have given a set of 226 faults. Smaller fault set can lead to more compact tests. Collapsing for the cell-based design of benchmark circuit, c499, reduces a set of 2,710 faults to just 586 faults.