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Sub-Doppler laser cooling requires optical pumping among differently light-shifted ground-state sublevels. We describe a study of the simplest possible angular-momentum configuration that permits all sub-Doppler cooling phenomena. The Jg =1 Je = 0 angular-momentum configuration shows recoil-limited cooling in the two most well-known types of polarization gradient, magnetically induced laser cooling, velocity-selective resonances, transient cooling, and velocity-selective population trapping.