  The shapes of relativistic iron lines observed in spectra of candidate black
holes carry the signatures of the strong gravitational fields in which the
accretion disks lie. These lines result from the sum of the contributions of
all images of the disk created by gravitational lensing, with the direct and
first-order images largely dominating the overall shapes. Higher order images
created by photons tightly winding around the black holes are often neglected
in the modeling of these lines, since they require a substantially higher
computational effort. With the help of the strong deflection limit, we present
the most accurate semi-analytical calculation of these higher order
contributions to the iron lines for Schwarzschild black holes. We show that two
regimes exist depending on the inclination of the disk with respect to the line
of sight. Many useful analytical formulae can be also derived in this
framework.
