In this paper the design criteria for antenna structures with improved radiation efficiency while operating in close vicinity to a biological scatterer are investigated. The study is performed using a simple λ/2 dipole combined with a directive or reflective element. The optimization criteria are the effective radiation efficiency, the spatial peak specific absorption rate (SAR), and the sensitivity of the input resistance to the distance from the scatterer. It is demonstrated that the primary design criterion to improve the radiation efficiency is not directivity but the reduction of the maximum incident magnetic field strength in the exposed skin area of the user's head. For the reflectively coupled dipole, all performance parameters are improved by several decibels compared to a standard, λ/2 dipole, whereas for some other directive structures, the performance is impaired. The study is conducted with the generalized multipole technique (GMT) numerical simulation method, the results of which are validated by measurement methods.