Power-Based Capon beamforming has recently been proposed to avoid the well-known cancellation effects between direct signal and correlated multipaths of the Capon beamformer. This novel technique exploits the fact that in some applications the power of the direct signal can be known at the receiver, in addition to the more usual assumptions of known spatial and temporal signatures. At the implementation stage, however, it involves solving a given two-dimensional rank minimization problem, which must be approximated to avoid inherent numerical limitations. In this work, we present an equivalent minimization problem that overcomes such limitations, and therefore leads to alternative implementations that can provide more precise and reliable results. The new approach is justified mathematically, and also supported by several simulations results.