Redundancy removal is an important step in combinational logic optimization. After a redundant wire is removed, other originally redundant wires may become irredundant, and some originally irredundant wires may become redundant. When multiple redundancies exist in a circuit, this creates a problem where we need to decide which redundancy to remove first. In this paper, we present an analysis and a very efficient heuristic to deal with multiple redundancies. We associate with each redundant wire a Boolean function that describes how the wire can remain redundant after removing other wires. When multiple redundancies exist, this set of Boolean functions characterizes the global relationship among redundancies.