We study the problem of cupping with random sets. Nies has shown that every random set below the halting problem has the strong random anticupping property via a promptly simple anticupping witness. We show that every set below the halting problem (not necessarily random) has the random anticupping property via a promptly simple anticupping witness. Moreover, we prove the following stronger statement: for every noncomputable Y below the halting problem there exists a promptly simple A such that if the join of it with a random is above Y then the random set is above A.