Given p?1, a subset A of a Banach space X is said to be p-limited if for every weakly p-summable sequence (xn*) in X* there exists (?n)??p such that |?xn*,x?|??n for all x?A and n?N. It is showed that p-limited sets are q-limited whenever p<q and Banach spaces enjoying the property that every q-limited subset is p-limited are characterized. We also prove that an operator has p-summing adjoint if and only if it maps relatively compact sets to p-limited sets. © 2013 Elsevier Inc.