Very recently, we were able to develop a new explanation for the emergence of hour-glass magentic spectra in cobalt oxides and to discard an alternative charge stripe scenario. In our nano phase separation scenario, the hour-glass dispersion arises from strongly de-coupled excitations within the undoped and within the hole-rich regions of nanometer size. Whereas Co ions within the nanometer-sized hole-rich regions are coupled with weak exchange interactions J', the Co ions within the nanoscopic undoped islands are coupled with much stronger exchange interactions J>>J' such that the hole-rich islands are not able to follow the magnetic excitations of the undoped islands to higher henergies.In order to get more quantitative experimental input for our entire nano phase separation model, we propose to study oxygen-doped cobaltates now. Compared to La2-xSrxCoO4 smaller exchange interactions can be expected in the La2CoO4+delta system at same hole-doping. Due to an altered size of the exchange interactions this proposed experiment will give complementary information that will help to understand the nature of the crossing of hour-glass spectrum in cobalates.