What to do about “next piece syndrome”?

Question

Inspired by this question: What to do about "stopping point syndrome"?

I often find myself a half hour away from knocking-off time having just wrapped up a component of my work, and facing a "next piece" that is going to take more than half an hour. (That's happening right now, as a matter of fact. Hence my surfing stackexchange during business hours!)

What do you do? Launch into the new piece knowing you'll have to stop in the middle? Set it aside and twiddle your thumbs until the clock runs out?