Any battery can me modeled as an ideal voltage source plus a complex impedance in series to it. This impedance has a real part and an imaginary part (reactive). The real part splits furthermore into two parts: a pure resistive part Rs (from few 1/100 of Ohms to 10 Ohms or more) depending on how big is the battery and a  RF lossy part which depends on the type of battery and on the frequency. Normally Rs can be measured or deduced from other measurements, while the lossy part is normally < Rs. Then comes the reactive part: normally at low frequencies (say at tenths of MHz) it is like a big capacitance in series to real part, but as frequency increases this reactive part can become inductive as happens in the case of electrolytic capacitors (a battery can be considered a very big capacitor !!). Generally lit-Ion batteries can be considered inductive above ~50-100 MHz. Hope this short memory will help you.....73s de IT9JCB

I thank you all for lot of interesting posts with  suggestions. Summarizing these posts they can be split into three classes:

1. A short vertical with counterpoints
2. A short horizontal dipole
3. A 'as long as possible' random wire plus tuner

There are many different opinions about this topic hi..hi.
As I pointed out in my first post the long wire solution is not applicable to my environment, I've a very small garden, a long balcony and a small roof where I've mounted my vertical for the others band (40..10m). I've already tried a 20 feet loaded wire sloping down to the garden with very poor results. The short horizontal dipole for me will suffer too much of ground proximity effects resulting in a too high take-off angle (the dipole will be at about 15-18 feet above ground i.e. lambda/12..).
To be honest, I like the vertical, but not too short (say about 12-15 feet) plus a proper matching unit in its base. Is there in the market a vertical like this ?

73s de IT9JCB

Thanks Phil,
I'm sorry I cannot do this....I can extend only about 20 foots of wire down to the garden but I've already tried this solution and it doesn't work at all. 73s Claudio

If you can accept little shadowed directions, even one resonant (i.e. lambda/4) radial will work well and even better than 4 rads in the right direction. I have one radial per band in my 14AVQ vertical, roof mounted at 15 meters over the ground...no problems to work dx down to 40m. 73s de IT9JCB

I've not enough space in the garden nor in my roof for an 80m band antenna, only balcony is available and I would operate on this band with decent results. I'm not looking for dx or pile-up, simply get in touch with my local friends within 300miles range. Do you have any suggestion  for this....someone suggested me a short vertical made-up  by a fiberglass fishing rod...??  73s IT9JCB

I've got ft-950 five days ago (see also my review on this site) and I've also tested the ic756pro-II (old version) in my friend's shack: there is no story ..756 outperforms ft-950 in all, but it costs about 1500$ more...!!! FT-950 has very good rf front-end, same of 756, same selectivity, and is a champion for quality/price, but when you are working with a low sig embedded in the noise the 756 plus its fantastic DNR is unsurpassed. Note that on 950 the DNR does not work at all..and least but not last: you can not engage it directly front the front buttons but via menu only.
Thinking to change my FT-950 soon with icom 756proIII....