Suppose Tukey's 3R (“running median”) smoothing algorithm is applied to a strictly stationary sequence X: = (Xk) of random variables, thereby creating a new stationary sequence Xœ IfXsatisfies the strong (Rosenblatt) mixing condition, then so does .Xœ If X is an i.i.d. sequence with each X(k:) uniformly distributed on the interval [0,1], then Xœ fails to be (mixing. Thus two questions ofC. Mallows are answered.