Cognitive radars are systems capable of optimizing emission and processing by exploiting knowledge about environment and operational scenario. Those improvements are achieved by controlling new degrees of freedom offered by modern radar technology. In particular, active phased-array radars can perform bidimensional beam-steering and beam-forming. Those new capabilities allow adaptation of radar search patterns to localized constraints. We present an improvement from our previous set cover approximation for radar search pattern time-budget minimization, accounting for localized constraints of terrain masking and direction-specific scan update rates. The addition of those constraints however does not modify the underlying mathematical structure of the problem, which can be solved using integer programming methods.