Let Y be a Banach space that has no finite cotype and p a real number satisfying 1 ≤ p < ∞ . We prove that a set ℳ ⊂ Π p ( X , Y ) is uniformly dominated if and only if there exists a constant 0$"> C > 0 such that, for every finite set { ( x i , T i ) : i = 1 , … , n } ⊂ X × ℳ , there is an operator T ∈ Π p ( X , Y ) satisfying π p ( T ) ≤ C and ‖ T i x i ‖ ≤ ‖ T x i ‖ for i = 1 , … , n .