If \((G,\Omega)\) is a permutation group, then the movement \(\text{move}(G)\) is the supremum of \(\{|\Gamma^g\setminus\Gamma|:\Gamma\subseteq\Omega,\;g\in G\}\). If \(G\) has no fixed points, \(n:=|\Omega|\), and \(\text{move}(G)=m\) is finite, then \(n\leq 5m-2\), by a result of \textit{C. E. Praeger} [J. Algebra 144, No. 2, 436-442 (1991; Zbl 0744.20004)]. Furthermore, by a result of Cho, Kim, and Praeger, equality holds if and only if \(n=3\) and \(G\) is transitive. In the present paper, the bound is improved. The authors show that if \(G\) has no fixed points and \(\text{move}(G)=m\) then \(n\leq(9m-3)/2\), and that equality holds infinitely often. The examples where equality holds are classified: if \(n>3\) then \(G\) is an elementary Abelian \(3\)-group, and all its orbits have size 3.