  We present a constructive approach to obtain information about the
compactness and shape of large-scale lowest excitations in disordered systems
by studying order-parameter fluctuations (OPF) at low temperatures. We show
that the parameter $G$ which measures OPF is 1/3 at T=0 provided the ground
state is unique and the probability distribution for the lowest excitations is
gapless and with finite weight at zero-excitation energy. We then apply
zero-temperature scaling to describe the energy and volume spectra of the
lowest large-scale excitations which scale with the system size and have a
weight at ze ro energy $\hat{P}_v(0)\sim l^{-\theta'}$ with $v=l^d$. A
low-temperature expansion reveals that, OPF vanish like $L^{-\theta}$, if
$\theta> 0$ and remain finite for space filling lowest excitations with
$\theta=0$. The method can be extended to extract information about the shape
and fractal surface of the large-scale lowest excitations.
