Let \(A\) be a uniform algebra on a compact Hausdorff space \(X\). Let \(m\) be a representing measure with support in \(X\) for a non-zero complex homomorphism on \(A\). The abstract Hardy space \(H^2=H^2(m)\) is defined as the closure of \(A\) in \(L^2(m)\). Special cases, where \(A\) is the disc algebra, are the classical Hardy space \(H^2\) and the Bergman space. For \(\phi\in L^\infty\), denote by \(T_\phi:L^2\to H^2\) the Toeplitz operator associated to \(\phi\) and let \({\mathcal C}(C(X))\) be the commutator ideal of the algebra generated by \(\{T_\phi,\phi\in C(X)\}\). Also, let \({\mathcal {LC}}(H^2)\) denote the compact operators on \(H^2\). In this paper, it is shown that if \({\mathcal C}(C(X))={\mathcal {LC}}(H^2)\), then the existence of a \(q\in A\) such that \(T_q\) is a non-unitary isometry implies some analytic structure on the maximal ideal space \(M(A)\). Also, the existence of a \(q\in A\) which is an essential isometry and is bounded below implies a similar conclusion. Special cases of this are respectively the classical Hardy space and the Bergman space, where one can take \(q=z\).