We present NEWMIN, an efficient cube-based algorith,m for minzmzzation of szngle Boolean functions. The salient features of the algorithm are that it does not generate all the prime cubes, and highly efficient heurastics are used to obtain a mznamal SPC cover. This leads to savzngs in computation tame and reduces the cost of the solution as well for some classes of funciions. The performance of a prototype implementation of MEIFMIN zs compared to that of ESPRESSO, the best known logic minzmizer currently available. Our algorathm efficiently handles Achilles' heel functions which ESPRESSO finds difficult. Further, as is evident from the results, XEWMIiV exhzbits better performance on several classes of functions such as parity junctions, cyclzc functions and most randomly generated functions.