This wouldn't normally be worth mentioning.
But it's an ATtiny28, which only implements a rather archaic version of High Voltage Parallel programming.
And my STK500 doesn't seem to be working.
So first I had to build a high voltage parallel programmer.
And implement firmware that would talk to something, because I sure can't tell how to get AVRDude to talk to something that implements HVPP :-(
In the process, I seem to have erased the signatures from two of my Tiny28s. Which is "interesting", since they otherwise still program fine and run the blinky code.