The Los Alamos Sferic Array (LASA) recorded VLF/LF electric-field-change signals from over ten million lightning discharges during the period from 1998 to 2001. Using the differential-times-of-arrival of lightning sferics recorded by three or more stations, the latitudes and longitudes of the source discharges were determined. Under conditions of favorable geometry and ionospheric propagation, sensors obtained ionospherically reflected skywave signals from the lightning discharges in addition to the standard groundwave sferics. In approximately 1% of all waveforms, automated processing identified two 1-hop skywave reflection paths with delays indicative of an intracloud (height greater than 5 km) lightning source origin. For these events it was possible to determine both the height of the source above ground and the virtual reflection height of the ionosphere. Ionosphere heights agreed well with published values of 60 to 95 km with an expected diurnal variation. Source height determinations for 100,000+ intracloud lightning events ranged from 7 to 20 km AGL with negative-polarity events occurring above ~15 km and positive-polarity events occurring below ~15 km. The negative-polarity events are at a suprisingly high altitude and may be associated with discharges between the upper charge layer of a storm and a screening layer of charge above the storm. Approximately 100 of the intracloud events with LASA height determinations were also recorded by VHF receivers on the FORTE satellite. Independent FORTE source height estimates based on delays between direct and ground-reflected radio emissions showed excellent correlation with the VLF/LF estimates, but with a +1 km bias for the VLF/LF height determinations.