  Doppler cooling on a narrow transition is limited by the noise of single
scattering events. It shows novel features, which are in sharp contrast with
cooling on a broad transition, such as a non-Gaussian momentum distribution,
and divergence of its mean square value close to the resonance. We have
observed those features using 1D cooling on an intercombination transition in
strontium, and compared the measurements with theoretical predictions and Monte
Carlo simulations. We also find that for a very narrow transition, cooling can
be improved using a dipole trap, where the clock shift is canceled.
