A family P={π1,…,πq} of permutations of [n]={1,…,n} is completely k-scrambling [Spencer, 1972; Füredi, 1996] if for any distinct k points x1,…,xk∈[n], permutations πi's in P produce all k! possible orders on πi(x1),…,πi(xk). Let N∗(n,k) be the minimum size of such a family. This paper focuses on the case k=3. By a simple explicit construction, we show the following upper bound, which we express together with the lower bound due to Füredi for comparison. 2 log2elog2n≤N∗(n,3)≤2log2n+(1+o(1))log2log2n. We also prove the existence of lim. Determining the value c_3 and proving the existence of \lim_{n \to \infty} N^{\ast}(n,k) / \log_2 n = c_k for k \geq 4 remain open.