I was bored, but not quite up to the challenge of debugging my existing radio project, or starting a new one. I idly began winding some wire onto a FT-37-43 toroid, and then remembered that I had never constructed a "Joule Thief", a simple little circuit that allows you to light an LED using just a 1.5 volt cell.
Addendum: I mentioned that legendary hacker Jeri Ellsworth had mentioned this circuit in one of her videos: I dug around and found the video. Her circuit is nearly identical, but adds a few components to implement a simple charging circuit.
I also did some experimentation with LTSpice to figure out why the lithium coin cells I scrounged from our old "throwies" didn't light the circuit, even though they still measured 1.5v. It appears that these coin cells might have significant series resistance (perhaps as much as 30 ohms) compared to the much lower value for alkaline batteries (a nominal 150 to 300 milliohms, according to one datasheet I found). This appears to keep the transistor from supplying sufficient current to switch. I experimented with placing a capacitor across the coin cell (various values, from 33uF to 220uF electrolytics) and found that this did cause the LEDs to blink, but at a very low rate (with a 220uF, about 1Hz). I'll try to follow up this post with one showing LTSpice and its simulation.