Process for obtaining polyethylene with an MFI (190° C./2.16 kg) of at least 4 g/10 minutes and a melt strength (190° C.) of at least 8.0 cN, said process involving extrusion of low density polyethylene (LDPE) with an MFI of at least 5 g/10 minutes and a vinyl content of less than 0.25 terminal vinyl groups per 1000 C-atoms (measured with NMR in deuterated tetrachloroethane solution)—in the presence of 500-5,000 ppm, based on the weight of low density polyethylene, of an organic peroxide.