This paper investigates phasor measurement unit (PMU) placement for informative state estimation in smart grid by incorporating various constraints for observability. Observability constitutes an important information-theoretic characteristic for PMU placement to reply the depth of the buses’ reachability by the placed PMUs, but addresing it solely by binary linear programming in many works still does not guarantee a good estimate for the grid state. Some existing works considered optimization problems of some estimation indexes by ignoring the observability requirements for computational ease and thus potentially lead to trivial results such as acceptance of the estimate for an unobserved state component as its unconditional mean. In this work, the PMU placement optimization problem is considered by minimizing the mean squared error or maximizing the mutual information between the measurement output and grid state subject to observability constraints, which incorporate operating conditions such as presence of zero injection buses, contigency of measurement loss, and limitation of communication channels per PMU. The proposed design is thus free from the fundamental shortcomings in the existing PMU placement designs. The problems are posed as large scale binary nonlinear optimization problems involving thousands binary variables, for which this paper develops efficient algorithms for computational solutions. Their performance is analyzed in detail through numerical examples on large scale IEEE power networks. The solution method is also shown to be extended to AC power flow models, which are formulated by nonlinear equations.