A method and a wireless device (110) for managing an EPS bearer, a method and a radio base station (120) for setting parameters of an S1 bearer or an Iu bearer as well as a method and a second network node (150) for managing an EPS bearer are disclosed. The wireless device (110) sends, to the second network node (150), a request for setting up the EPS bearer for a service. The request is associated with a required level of a connectivity for the service. The required level relates to likelihood of maintaining the connectivity towards a first network node (140). The second network node (150) further receives the required level of the connectivity for the service. The second network node (150) sends, to a radio base station (120), a request for setting parameters of the S1 bearer or the Iu bearer. Corresponding computer programs and computer program products are also disclosed.