Given a real number 0.a 1 a 2 a 3 . . . that is normal to base b, we examine increasing sequences n i so that the number 0.a n1 a n2 a n3 . . . are normal to base b. Classically, it is known that if the n i form an arithmetic progression, then this will work. We give several more constructions including n i that are recursively defined based on the digits a i. Of particular interest, we show that if a number is normal to base b, then removing all the digits from its expansion which equal (b − 1) leaves a base-(b − 1) expansion that is normal to base (b − 1)