Dead-time effects in X-ray spectra taken with a digital pulse processor and a silicon drift detector were investigated when the number of events at the low-energy end of the spectrum was more than half of the total, at counting rates up to 56 kHz. It was found that dead-time losses in the spectra are energy dependent and an analytical correction for this effect, which takes into account pulse pile-up, is proposed. This and the usual models have been applied to experimental measurements, evaluating the dead-time fraction either from the calculations or using the value given by the detector acquisition system. The energy-dependent dead-time model proposed fits accurately the experimental energy spectra in the range of counting rates explored in this work. A selection chart of the simplest mathematical model able to correct the pulse-height distribution according to counting rate and energy spectrum characteristics is included.