Running Arduino-compatible from batter(y|ies) without regulator

PaulS:

Given Jeenodes are running at 3.3v and regular Arduinos at 5V I had the impression that the voltage could be anywhere in the range from 3.3v to 5v and from the thread I linked to, perhaps even a wider range than this.

With suitable changes to fuse settings, the Arduino can run at either 3.3V or 5V, not any random value in between.

Do you have any source for this? Page 316 of the datasheet here shows a curve between maximum clock speed and voltage. Notice that it is a curve, and shows the maximum clock range for every voltage between 1.8V and 5.5V -- not just 3.3V and 5V as you seem to suggest. Furthermore, except for the BOD fuse -- which could be disabled completely for non-critical applications -- no fuses need to be changed for a change in voltage. I'm not completely sure about this part, but you showed no source either.

clock speed, which is a function of voltage.

Clock speed is a function of the crystal one puts on the chip. True, the maximum clock speed changes, but as long as the speed is under the maximum for the minimum voltage one will have (or if one doesn't mind overclocking) the voltage does not affect clock speed. Notice that standard crystals you can buy don't have specific voltage written on them.