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A heuristic method to obtain near-minimal covers of p-valued switching functions is introduced. First, we describe transform tools useful in the processing of MVL functions. They are: p-adic shifting, weighting, and implicant detecting transformations. Based on these tools, a direct cover algorithm is presented that uses local information for heuristic decision making. The heuristics are taken from weight coefficients calculated for canonical terms and implicants. The method allows to assign cost factors to implicants. Further, the algorithms can be modified easily, so as to correspond to various connectives (e.g., MAX, PLUS).