Abstract. Galactic maps of e− e + annihilation radiation based on CGRO-OSSE, SMM and TGRS data have indicated the existence of an extended component at positive Galactic latitudes (l ≈ −2• , b ≈ 7 • ), in addition to the emission from the galactic bulge and disk (Purcell et al. 1997;Cheng et al. 1997;Milne et al. 2000;Milne et al. 2001). This Positive Latitude Enhancement (PLE) was first attributed to an "annihilation fountain" in the Galactic center (Dermer & Skibo 1997) but has since been the object of several models. After discussing the observational evidence for the PLE, we investigate various models for the PLE: besides the scenarios proposed in the literature, we have introduced a number of models requiring relatively modest positron rates due to a local origin of the e − e + emission (local galactic-, solar system-, earth-and spacecraft-environment origins). The various scenarios for the PLE are constrained in the light of the latest OSSE-SMM-TGRS data analysis results: we have looked at the possible positron production mechanisms as well as the annihilation conditions in the different physical environments (temperature and dust grain content) proposed for the positive-latitude region. By constraining those parameters, based on the recent limits for the line width and the positronium fraction, we found that some of the models can essentially be discarded. A number of other scenarios will have to await further measurements and maps, such as will be possible with INTEGRAL's SPI and IBIS instruments. We present a table/checklist of model-falsification criteria.