Previously finding prime implicants based on off-cubes was explored as an approach to minimize insignificant logic functions which include minterms both easy and difficult to cover. Off-cube based function minimization falls short in certain functions and may not yield/produce the accurate results. In this study, a new method of minimizing insignificant logic functions that includes smart minterm ordering according to their contiguity is proposed. In the proposed method, minterms are ordered from easy to difficult in terms of covering. This kind of a smart ordering helps minimization algorithms to quickly cover easy minterms and decrease the complexity of remaining function. A new accumulation approach is also developed and employed for the minimization of complicated functions. The use of the new accumulation approach in the study made it possible to reach more precise results. When it is impossible to determine exact prime implicants, the developed algorithm accumulates minterm and its corresponding implicants in a suspended state (SS) and reconsiders covering them later. Both the theory and practice of accumulation approach for the minimization of minterms is presented. Standard MCNC benchmarks are simplified with both the proposed method and with the two level simplification program ESPRESSO. The comparative analysis of the results revealed that the proposed method finds exact minimum results using less time and memory than ESPRESSO.