Here we report the first series of phase-pure zinc-blende CdSe/CdS core/shell quantum dots (QDs) with reproducibly controlled shell thickness (4-16 monolayers), which are nonblinking (>= 95% 'on' time) in single-exciton regime for the entire series. These unique QDs possess well-controlled yet simple excited-state decay dynamics at both single-dot and ensemble levels, extremely small nonblinking volume threshold, if any, and unique 'on' and 'off' probability statistics. The outstanding optical properties of the QDs at the single-dot level were found to be correlated well with their ensemble properties. These small and bright nonblinking QDs offer promising technical application prospect in both single-dot and ensemble levels. The consistent and reproducible experimental results shed new light on the mechanisms of blinking of QDs.