Causal models communicate our assumptions about causes and e ects in real-world phenomena. Often the interest lies in the identification of the e ect of an action which means deriving an expression from the observed probability distribution for the interventional distribution resulting from the action. In many cases an identifiability algorithm may return a complicated expression that contains variables that are in fact unnecessary. In practice this can lead to additional computational burden and increased bias or ine ciency of estimates when dealing with measurement error or missing data. We present graphical criteria to detect variables which are redundant in identifying causal e ects. We also provide an improved version of a well-known identifiability algorithm that implements these criteria.