  Let $A$ be any plane set. It is known that a holomorphic motion $h: A \times
\mathbb{D} \to \mathbb{C}$ always extends to a holomorphic motion of the entire
plane. It was recently shown that any isotopy $h: X \times [0,1] \to
\mathbb{C}$, starting at the identity, of a plane continuum $X$ also extends to
an isotopy of the entire plane. Easy examples show that this result does not
generalize to all plane compacta. In this paper we will provide a
characterization of isotopies of uniformly perfect plane compacta $X$ which
extend to an isotopy of the entire plane. Using this characterization, we prove
that such an extension is always possible provided the diameters of all
components of $X$ are uniformly bounded away from zero.
