For the Sturm-Liouville problem \[ -y'' +q y = \lambda w y\text{ on }[a,b] \] with separated selfadjoint boundary conditions the inverse spectral question whether the potential \(q \in L^1(a,b)\) is uniquely determined by the spectrum is discussed. For the right definite case \(w > 0\), there are known results using two additional eigenvalue problems with an intermediate endpoint [e.g. \textit{F. Gesztesy} and \textit{B. Simon}, ``On the determination of a potential from three spectra'', Transl., Ser. 2, Am. Math. Soc. 189(41), 85--92 (1999; Zbl 0922.34008); \textit{V. A. Pivovarchik}, ``An inverse Sturm-Liouville problem by three spectra'', Integral Equations Oper. Theory 34, No.~2, 234--243 (1999; Zbl 0948.34014)]. In the present paper, these results are extended to the indefinite case \(xw(x) > 0\) where \(a < 0 < b\) and \(|w|' \in AC(a,b)\). In addition to the original eigenvalue problem, also the problems induced by \[ -y'' +q y = \lambda w y\text{ on }[a,0]\text{ and on }[0,b] \] are considered where the original boundary conditions are imposed at \(a\) and \(b\) and a new (separated) condition is imposed at \(0\). As the main result it is shown that \(q\) is uniquely determined by the three spectra associated with the three problems under the condition that these spectra are pairwise disjoint. A consequence of this result is formulated for the left-definite case where \(q \geq 0\). Then a condition is obtained using (more or less) only the greatest eigenvalue of the problem on \([a,0]\) and the smallest eigenvalue on \([0,b]\).