In light of recent experimental results, we carefully analyze the effects of interference in neutrinoless double beta decay, when more than one mechanism is operative. If a complete cancellation is at work, the half-life of the corresponding isotope is infinite and any constraint on it will automatically be satisfied. We analyze this possibility in detail assuming a cancellation in 136-Xe, and find its implications on the half-life of other isotopes, such as 76-Ge. For definiteness, we consider the role of light and heavy sterile neutrinos. In this case, the value of the redefined effective Majorana mass parameter gets suppressed, and a larger values of neutrino masses are required for the same half-life. As a result, where all the sterile neutrinos are heavy, the tension between the results from neutrinoless double beta decay and cosmology becomes even more severe, than the canonical light neutrino case. We show that the inclusion of light sterile neutrinos in this set up can resolve this issue. Using the recent results from GERDA, we derive upper limits on the active-sterile mixing angles and compare it with the case of no cancellation. The required values of the mixing angles become larger, if a cancellation is at work. We show that the sterile neutrinos of few hundred MeV or GeV mass range, coming from an Extended seesaw framework or a further extension, can satisfy the required cancellation.