We study the conductance (g) distribution function of an ensemble of isolated conducting rings, with an Aharonov-Bohm flux. This is done in the discrete spectrum limit, i.e. when the inelastic rate, frequency and temperature are all smaller than the mean level spacing. Over a wide range of g the distribution function exhibits universal behaviour P(g) ~ g ~(4 where /3 = 1 (2) for systems with (without) a time reversal symmetry. The non-universal large-gr tail of this distribution determines the values of high moments.