In this paper we study the following problem: we are given a certain region R to monitor and a requirement on the degree of coverage (DoC) of R to meet by a network of deployed sensors. The latter will be dropped by a moving vehicle, which can release sensors at arbitrary points within R. The node spatial distribution when sensors are dropped at a certain point is modeled by a probability density function F. The network designer is allowed to choose an arbitrary a set of drop points, and to release an arbitrary number of sensors at each point. Given this setting, we consider the problem of determining the optimal grid deployment strategy, i.e., the drop strategy in which release points are arranged in a grid such that (1) the DoC requirement is fulfilled and (2) the total number of deployed nodes n is minimum. This problem is relevant whenever manual node deployment is impossible or overly expensive, and partially controlled deployment is the only feasible choice. The main contribution of this paper is an accurate study of the interrelationships between environmental conditions, DoC requirement, and cost of the deployment. In particular, we show that, for a given value of σ and DoC requirement, optimal grid deployment strategies can be easily identified.