We present new techniques for explicit constraint satisfaction in the incremental placement process. Our algorithm employs a Lagrangian Relaxation (LR) type approach in the analytical global placement stage to solve the constrained optimization problem. We establish theoretical results that prove the optimality of this stage. In the detailed placement stage, we develop a constraint-monitoring and satisfaction mechanism in a network (n/w) flow based detailed placement framework proposed recently, and empirically show its near-optimality. We establish the effectiveness of our general constraint-satisfaction methods by applying them to the problem of timing-driven optimization under power constraints. We overlay our algorithms on a recently developed unconstrained timing-driven incremental placement method FlowPlace. On a large number of benchmarks with up to 210K cells, our constraint satisfaction algorithms obtain an average timing improvement of 12.4% under a 3% power increase limit ...