Zener Diode Effect in Series

Sure you don't mean "forward bias mode"?

A Zener diode is usually used in reverse bias mode (cathode to positive); it won't conduct significantly until the Zener voltage is reached. In forward bias mode (anode to positive), it behaves like a "normal" diode. The forward voltage drop (Vf) depends on the particular device.

Good old Wiki....

If wired in one direction it will drop about 0.7v if wired the other way around it will drop the zenner voltage.
The best thing is to get a 3v3 zenner or similar a 1k resistor, a pp3 battery and a volt meter. You can then play until you are contented.

On some input circuits I use two 4v7 zenners wired in seried back to back across the input terminals to help remove spikes to protect the input to a microprocessor. so any voltage over 4.7 + 0.7 will be conducted regardless of the spike polarity (I realise that the series impedance is still fairly high and this doesn't provide sophisticated protection...but it helps in some applications)
Del