The lower ionosphere is difficult to access from the ground, but also in-situ measurements by sounding rockets have their limitations. The semi-empirical model of the non-auroral ionosphere FIRI (= Faraday-IRI) was originally published in 2001 and is based on a simple ion-chemical model of the lower ionosphere whose output is adjusted by the limited number of reliable in-situ rocket measurements, all based on wave propagation methods. Since then some of the data were found to be questionable, but could be replaced by about the same number of trustworthy data. In addition, a large number of electron density profiles based on Langmuir probes became available covering the altitude range from 51 to 90 km. These data are used to extend FIRI downward providing results in a region that would otherwise not be covered at all. Caution was taken that these data do not impair the altitudes covered by wave propagation data which are unaffected by aerodynamic and payload potential effects. The resulting semi-empirical model is available as 1980 profiles of electron densities between 60 and 150 km altitude (for 11 solar zenith angles from 0 to 130°, latitudes 0, 15, 30, 45 and 60°, for three solar activities and the middle of the each month).