X-ray emissions associated with leaders of natural cloud-to-ground lightning are examined. For 23 (8 first and 15 subsequent) strokes within 2 km of the Lightning Observatory in Gainesville, the occurrence of detectable X-rays was 88% and 47% for the first and subsequent strokes, respectively. Some subsequent-stroke leaders, retracing previously formed, low-density channels, are more prolific producers of detectable X-rays than their corresponding first-stroke leaders, developing in the virgin air. The energy of some photons was in the MeV range (in one case possibly in excess of 5 MeV); that is, in the gamma-ray range. There was a significant difference between first and subsequent leaders in terms of the distribution of estimated X-ray source heights. For first leaders, the maximum source height did not exceed 800 m, whereas for subsequent leaders the source height distribution appeared to extend to about 3.6 km. Not all leaders within a flash produced detectable X-rays. For the same leader near ground, some steps were accompanied by detectable X-ray emissions, while others were not. One possible explanation is that electric field enhancements (>30 MV/m or so for the case of normal air density), needed for the cold runaway breakdown, are very brief and highly localized, so that in many cases a sufficiently energetic electron from the tail of the bulk distribution may be unavailable to start the runaway process. This implies that the cold runaway breakdown is not a necessary feature of lightning leaders, even if the required fields do occur.