<p>This paper is devoted to the study of <i>disjoint p-limited completely continuous</i> (d<i>p</i>-lcc) operators, a new class of operators naturally associated with the notion of <i>p</i>-limited sets in Banach lattices. We establish connections between this new class of operators with other limited-type completely continuous classes of operators on Banach lattices. A new Gelfand–Phillips-type property related to the d<i>p</i>-lcc operators is defined. As an application of our results, we provide necessary and sufficient conditions under which the adjoint of every positive d<i>p</i>-lcc operator between two given Banach lattices is also d<i>p</i>-lcc. We also obtain the duality results for others limited-type completely continuous operators.</p>