Embodiments herein relate to a method for controlling transmit power of a mobile terminal. The method is performed by a mobile terminal in a dual connectivity mode wherein the mobile terminal is configured to support two or more contemporaneous links, including a first link and a second link, with two or more wireless network access points. The mobile terminal independently calculates a respective unscaled uplink transmission power level for each link, based on a corresponding link-specific value. The mobile terminal calculates a respective scaling factor for each link based on a total-power constraint and on one or more of the following: uplink resource allocation to each link, such that the scaling factor for the first link allocated more resources than the second link is larger than the scaling factor for the second link, link quality for each link, such that the scaling factor for the first link having a better link quality than the second link is larger than the scaling factor for the second link, uplink buffer state for each link, such that the scaling factor for the first link having more uplink data to be sent than the second link is larger than the scaling factor for the second link, and priority for each link, such that the scaling factor for the first link having a higher priority than the second link is larger than the scaling factor for the second link. The mobile terminal further applies the respective scaling factor to each respective unscaled uplink transmission power level, to obtain corresponding scaled power levels. The mobile terminal furthermore transmits over the two or more contemporaneous links at the respective scaled power levels.