By appropriately selecting their relaying partners, wireless users are able to reduce their average transmit power without any performance cost. This important feature of cooperation is captured by the notion of relaying efficiency: A relaying partner is considered efficient for a given user if it can decrease the overall transmit power for achieving a certain signal-to-noise ratio (SNR) associated with that user. In this work, a two-dimensional geometric investigation of efficient cooperation is conducted. It is shown that the locus of efficient partner locations can be approximated by an ellipse, which is centred at the midpoint of the user and the base station, and has an eccentricity which depends on the path loss exponent. Moreover, the efficiency of the relaying partners is illustrated via contour graphs, which provide a graphical assessment of the energy efficiency potential of cooperation based on partner location. The cases of fading-free transmissions and transmission over Rayleigh fading channels are examined.