Because of the way LEDs are designed, If is going to increase with Vf, so the two are almost directly related. However, according to the Luxeon data sheets, Vf at a given current has a negative temperature coefficient which means constant voltage supplies can be dangerous. This is known as the thermal runaway effect. "Direct Drive" setups offer some protection, as you then rely on the battery's internal resistance to limit current. This is why you would not want to direct drive a setup with 3 D cells when it is designed for 3 AA cells; the D size cells have a lower internal resistance and can provide more current while maintaining voltage. A non-regulating step-up converter will simply reduce overall output power as its input voltage decreases. This design offers longer overall runtime but with no regulation, of course. A regulated design will draw more and more current from the battery supply (up to a certain point) which actually reduces overall runtime, but maintains a constant brightness throughout the discharge.
It all depends on what type of power supply you are using (regulated or non-regulated) and if it's non regulated, what kind of light output you want. My first post was on the understanding that the MicroPuck is regulated, which I hear now it is not...if you are interested purely in runtime, a parallel setup would work best with a non-regulated boost, but with less light output. A series setup would provide more initial light, with less runtime. A series setup is also the best way to drive a regulated power supply. So...it all boils down to, do you want more initial light, or is less light but longer runtime desired? Or, reasonable runtime with constant light output?
On the flipside, operating a buck-type regulator is far more efficient than a boost-type regulator. This is because the buck regulator merely switches current on and off through an inductor, it being used only to smooth out the pulses...boost regulators must "charge" the inductor by connecting it directly across Vin and then switching it in series with Vin so the voltage pulse from the inductor + Vin = Vout.
As for driving in paralell, be careful...variations in Vf from LED to LED can cause some to "hog" current, resulting in overdriven LEDs and reduced lifetime.
