The recent rise of interest in distributed applications has highlighted the importance of effective information dissemination. The challenge lies in the fact that nodes in a distributed system are not necessarily synchronized, and may fail at any time. This has led to the emergence of randomized rumor spreading protocols, such as push and pull protocols, which have been studied extensively. The k-pull operation, which allows an uninformed node to ask for the rumor from a fixed number of other nodes in parallel, has been proposed to improve the pull algorithm's effectiveness. This paper presents and studies the performance of the k-pull operation in the presence of a certain fraction f of non-cooperative nodes. Our goal is to understand the impact of k on the propagation of the rumor despite the presence of a fraction f of non-collaborative nodes.