While the axiomatic system P is an important standard for plausible nonmonotonic reasoning, inference relations obtained from system Z or from c-representations have been designed which go beyond system P. In this paper, we propose the new concept of weakly skeptical inference that properly extends the recently introduced skeptical c-inference, but avoids disadvantages of a too liberal credulous inference. We extend the concepts of skeptical, weakly skeptical, and credulous c-inference by taking preferred models obtained from different minimality criteria into account. We illustrate the usefulness of the obtained inference relations, show that they fulfill various desirable properties, and elaborate on their interrelationships.