Beamforming schemes have been proposed to exploit the spatial characteristics of multiple-input single-output (MISO) wireless radio channels. Several algorithms are available for optimal joint beamforming and power control for the downlink. Such optimal beamforming minimizes the total transmission power, while ensuring an individual target quality of service (QoS) for each user; alternatively the weakest QoS is maximized, subject to a power constraint. Herein, we consider both formulations and some of the available algorithms are generalized to enable indefinite quadratic shaping constraints on the beamformers. By imposing such additional constraints, the QoS measure can be extended to take other factors than the customary signal-to-interference-and-noise ratio (SINR) into account. Alternatively, other limitations such as interference requirements or physical constraints may be handled within the optimization. We also consider a more general SINR expression than previously analyzed, which allows for more accurate modeling, e.g., of nonzero self-interference in code-division multiple-access (CDMA) systems. Several applications for indefinite equality or inequality constraints are suggested and evaluated. For example, it is shown how such constraints may be used to ensure a minimum level of path diversity in a CDMA system. Other applications include limiting intercell interference in decentralized systems