Cokriging allows predicting coregionalized variables from sampling information, by considering their spatial joint dependence structure. When secondary covariates are available exhaustively, solving the cokriging equations may become prohibitive, which motivates the use of a moving search neighborhood to select a subset of data, based on their closeness to the target location and the screen effect approximation. This paper investigates the efficiency of different strategies for designing a sub-optimal neighborhood wherein the simplification of the cokriging equations is challenging. To do so, five alternatives (single search, multiple search, strictly collocated search, multi-collocated search and isotopic search) are tested and compared with the reference unique neighborhood, through synthetic examples with different data configurations and spatial joint correlation models. The results indicate that the multi-collocated and multiple searches bear the highest resemblance to the reference case under the analyzed spatial structure models, while the single and the isotopic searches, which do not differentiate the primary and secondary sampling designs, yield the poorest results in terms of cokriging error variance.