The Laws of Arising in the Morning (16)

1. Washing one’s hands without a cup (for example if he rubs his hands in water), helps to allow him to say the Shema and to pray, and even to say the Berachah “Al netilas yadayim”, but it does not help to remove the evil spirit. Therefore, one should wash one’s hands from a cup (or another vessel) even if one has already prayed. (Shulchan Aruch and Mishne Berura 4)

2. If he rubs his hands three times, in three separate bowls full of water, the halachah is unclear, and it is possible that it helps even to remove the evil spirit from his hands. (Mishne Berura ibid)