  We study the statistics of the reflectance (the ratio of reflected and
incident intensities) of an $N$-mode disordered waveguide with weak absorption
$\gamma$ per mean free path. Two distinct regimes are identified. The regime
$\gamma N^2\gg1$ shows universal fluctuations.
  With increasing length $L$ of the waveguide, the variance of the reflectance
changes from the value $2/15 N^2$, characteristic for universal conductance
fluctuations in disordered wires, to another value $1/8 N^2$, characteristic
for chaotic cavities. The weak-localization correction to the average
reflectance performs a similar crossover from the value $1/3 N$ to $1/4 N$. In
the regime $\gamma N^2\ll1$, the large-$L$ distribution of the reflectance $R$
becomes very wide and asymmetric, $P(R)\propto (1-R)^{-2}$ for $R\ll 1-\gamma
N$.

Condensed Matter