Can I power four leds in parallel with a single AA battery ?

Joule thieves seem really interesting. I have found a schematics using a 1:1 filtering transformer. It does also add a capacitor to smooth the signal and a diode to prevent backwards currents (please see first attached schematics, visible only if you're logged in - note that the transformer is shown as two coils because there's no drawing for transformers in Fritzing).

However as the signal has a very fast oscillation the voltage between the collector and the emitter can't be measured by a multimeter. An oscilloscope is needed and I don't have one.

So I was wondering if a Zener diode could help to set a specific voltage because I think the voltage I have now is too high for my four LEDs (even connected in series). With this capacitor (which has a value of 2.2 mF actually but I can't ge Fritzing to reflect this - it seems only presets values are possible for capacitances in this software) I get a voltage as high as 7.4 V between the terminals of the capacitor.

Please see second and third schematics. I don't know if either could be a solution (please note that the 4.8V for the Zener was chosen because the LEDs have a typical 1.2 Vf - forward voltage) but I am thinking about using a higher voltage for the Zener so to allow the insertion of a resistor in series with the LEDs.

Any comment over these schematics would be highly appreciated.