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Team problems over the set of affine team control laws are solved as constrained parameter optimization problems. This methodology eases both the notational and computational difficulties. For the LQGT (linear-quadratic-Gaussian team) and the LEGT (linear-exponential-Gaussian team) problems, the constrained parameter optimization approach leads to the representation of the optimal team control gains as explicit projections of the optimal centralized gains. The projection representation offers insight into the team solution and suggests an algorithm for computing the optimal gains for the LEGT problem. The LEGT problem behavior is compared to LQGT behavior for an example which consists of a static team with garbled decision implementation.