transformerless TCs/ would a variometer be useful?

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Jolyon Vater Cox by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jolyon-at-vatercox.freeserve.co.uk>

With regard to transformerless/ capacitive transformer Tesla coils, I cannot
help but think that where C1 is to be substituted for larger/smaller
capacitance it would be useful for L1 to be variable to facilitate re-tuning in
a similar to adjusting the primary tapping point on a conventional TC.
 
Does this not sound similar to adjusting the impedance match of an antenna to a
radio transmitter using an Antenna Matching Unit- except that with an AMU the
coils are largely fixed and fine tuning is done by a variable capacitor whereas
with a Tesla coil the reverse is usually the case.
 
In view of this and the fineness of tuning (does tuning on have to be this
fine?) would not the variometer-type of variable inductor be the best design
for L1 in a transformerless TC?
 
If the above is correct, does anyone have a design for a cheap, reliable
variometer, all the better if it were a small one- given the "miniature" nature
of my anticipated design
-L2 is only 5 5/16" tall and 1 1/8" in diameter and the final TC will
(hopefully!) be driven by no more than a flyback transformer.