Summary: We study the Banach spaces \(X\) for which the essential spectrum \(\sigma_{\mathrm{e}}(T)\) of every \(T\) in \(L(X)\) is finite. We show that there exists an integer \(n\) so that \(|\sigma_{\mathrm{e}}(T)| \leqslant n\) for every \(T\). We also show that \(X\) admits an irreducible decomposition as a direct sum of indecomposable subspaces, and that the quotient algebra \(L(X)/\mathrm{In}(X)\), \(\mathrm{In}(X)\) the inessential operators, is isomorphic to a finite product of spaces of scalar matrices.