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Due to the application-specific nature of sensor networks, sensing-quality control factors, such as coverage and delay, need to be parameterized in order to optimize energy conservation depending on the type of applications. An application-specific data gathering scheme is an example of such an application-specific algorithm design. In this scheme, only a minimum number of data reporters (sensors) are in each round randomly selected based on the desired sensing coverage (DSC) specified by the applications/users. In this paper, we investigate the use of the Poisson sampling technique which maintains a certain minimum distance between sampled points, to cope with an undesirable property that the selected data reporters may be located too closely. Then, based on this sampling technique we propose a constrained random sensor selection scheme, called CROSS. Inherently, the CROSS improves the spatial regularity of selected sensors, thus reducing the variance of the sensor covered area in each round. Consequently, the fidelity of meeting the DSC in each round improves. We present an algorithm to compute a desired minimum distance (DMD) to be forced between the selected sensors. Simulation results demonstrate that the DMD computed by our algorithm is almost optimal in terms of the improvement on the fidelity of meeting the DSC.