This paper identifies vulnerabilities to recently proposed countermeasures to leakage power analysis attacks in FDSOI systems based on the application of a random body bias. The vulnerabilities are analyzed and the relative difficulty to obtain the secret key, once the vulnerabilities are taken into account, are compared to the original proposals. A new countermeasure, based on a new body bias scheme, is then proposed. The new countermeasure is based on the equalization of asymmetries in static power consumption dependent on data being stored in registers implemented in FDSOI technology. The countermeasure’s effectiveness is theoretically established through the development of a power model based on technological parameters, and further reinforced through numerical simulations of a dummy cryptosystem implementing part of an AES encrypting round.