High harmonics driven by two-color counterrotating circularly polarized laser fields are a unique source of bright, circularly polarized, extreme ultraviolet, and soft x-ray beams, where the individual harmonics themselves are completely circularly polarized. Here, we demonstrate the ability to preferentially select either the right or left circularly polarized harmonics simply by adjusting the relative intensity ratio of the bichromatic circularly polarized driving laser field. In the frequency domain, this significantly enhances the harmonic orders that rotate in the same direction as the higher-intensity driving laser. In the time domain, this helicity-dependent enhancement corresponds to control over the polarization of the resulting attosecond waveforms. This helicity control enables the generation of circularly polarized high harmonics with a user-defined polarization of the underlying attosecond bursts. In the future, this technique should allow for the production of bright highly elliptical harmonic supercontinua as well as the generation of isolated elliptically polarized attosecond pulses.