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This work addresses the problem of joint downlink beamforming and power control with general quality of service (QoS) constraints. Previous work on downlink beamforming does not provide a framework to handle the additional constraints in a straightforward fashion. Herein, it is shown that the QoS requirements can be formulated as quadratic constraints to a convex optimization problem. An efficient algorithm for solving the problem, based on semidefinite optimization is presented. To demonstrate the performance of the proposed approach, we present an example using quadratic constraints to greatly decrease the probability of a low instantaneous signal to interference and noise ratio (SINR) for a receiver equipped with a RAKE combiner.