The iPod app in the iPhone does have a sleep timer, it turns out. It’s just that it’s so well hidden that I’d never have found it without clues from elsewhere.

To set an iPod sleep timer:

1. Enter the Clock application
2. Tap Timer in the bottom right-hand corner
3. Set a time using the odometer thing
4. In the ‘When Timer Ends’ menu, instead of an alarm sound, select ‘Sleep iPod’
5. Tap Start.

I had looked in the timer section of the clock app before — on the iPod, sleep timers are also set through the Clock menu item — but because I hadn’t explored the alarm-tone picker, I hadn’t spotted the ‘Sleep iPod’ option. Silly me, thinking that a menu wouldn’t logically contain 23 options all meaning ‘make noise’ and one option meaning ’stop making noise’.

Note that you cannot tell the iPod to start playing at a certain time. Though the Alarm function of the clock allows you to be awakened by any one of Apple’s canned ringtones, it won’t let you pick one of your own songs as the alarm sound.