  A formalism for treating the pile-up produced in solid-state detectors by
laser-driven pulsed x-ray sources has been developed. It allows the direct use
of x-ray spectroscopy without artificially decreasing the number of counts in
the detector, assuming the duration of a pulse is much shorter than the
detector response time and the loss of counts from the energy window of the
detector can be modeled or neglected. Experimental application shows that
having a small amount of pile-up subsequently corrected improves the
signal-to-noise ratio, which would be more beneficial than the strict
single-hit condition usually imposed on this detectors.
