We present an HST STIS spectrum of the HeII Gunn-Peterson effect towards HE2347-4342. Compared to the previous HST GHRS data obtained by Reimers et al. (1997), the STIS spectrum has a much improved resolution. The 2-D detector also allows us to better characterize the sky and dark background. We confirm the presence of two spectral ranges of much reduced opacity, the opacity gaps, and provide improved lower limits on the HeII G-P opacity in the high opacity regions. We use the STIS spectrum together with a Keck--HIRES spectrum covering the corresponding HI Lya forest to calculate a 1-D map of the softness S of the ionization radiation along the line of sight towards HE 2347-4342, where S is the ratio of the HI to HeII photoionization rates. We find that S is generally large but presents important variations, from S ~ 30 in the opacity gaps to a 1 sigma lower limit of 2300 at z~2.86, in a region which shows an extremely low HI opacity over a 6.5 A range. We note that a large S naturally accounts for most of the large SiIV to CIV ratios seen in other quasar absorption line spectra. We present a simple model that reproduces the shape of the opacity gaps in absence of large individual absorption lines. We extend the model described in Heap et al. (2000) to account for the presence of sources close to the line of sight of the background quasar. As an alternative to the delayed reionization model suggested by Reimers et al. (1997), we propose that the large softness observed at z~2.86 is due to the presence of bright soft sources close to the line of sight, i.e. for which the ratio between the number of HI to HeII ionizing photons reaching the IGM is large. We discuss these two models and suggest ways to discriminate between them.