  We study radiative linewidth of exciton resonance in shallow
In$_x$Ga$_{1-x}$As/GaAs single quantum wells as a function of indium
concentration in the range $x=0.02...0.10$ and well thickness in the range
$L_Z=1...30$ nm using the method of Brewster reflection spectroscopy. Record
linewidths of heavy-hole exciton resonance of about 130...180 $\mu$eV are
measured in reflection spectra for single quantum wells with $L_Z=2$ nm and
$x=0.02$ at temperature 9 K. In these spectra, the non-radiative linewidth
including inhomogeneous broadening can be comparable or even less than
radiative linewidth. It is shown that radiative linewidth weakly depends on $x$
and $L_Z$ in these ranges. In multiple-quantum-well Bragg structure with ten
periods radiative linewidth exceeds inhomogeneous broadening by 4 times.
