Efficient unification is considered within the context of logic programming. Unification is explained in terms of equivalence classes made up of terms, where there is a constraint that no equivalence class may contain more than one function term. It is demonstrated that several well-known "efficient" but nonlinear unification algorithms continually maintain the said constraint as a consequence of their choice of data structure for representing equivalence classes. The linearity of the Paterson-Wegman unification algorithm is shown largely to be a consequence of its use of unbounded lists of pointers for representing equivalences between terms, which allows it to avoid the nonlinearity of "union-find".