Nate the Great and the Pillowcase

It's two o'clock in the morning when the telephone rings and Nate the Great learns that Rosamond's pillowcase is missing. She needs it now because her cat, Big Hex, likes to sleep on it. Outside it is damp, dark, and dreary, but a good (yawning) sleuth knows that the hunt must go on. Can Nate the Great find the missing piece of laundry before the sun comes up, and before his bedroom slippers wear out?