  We derive quantitative bounds for eigenvalues of complex perturbations of the
indefinite Laplacian on the real line. Our results substantially improve
existing results even for real-valued potentials. For $L^1$-potentials, we
obtain optimal spectral enclosures which accommodate also embedded eigenvalues,
while our result for $L^p$-potentials yield sharp spectral bounds on the
imaginary parts of eigenvalues of the perturbed operator for all
$p\in[1,\infty)$. The sharpness of the results are demonstrated by means of
explicit examples.
