Integrated circuits with high-speed communications capabilities are provided. Such types of integrated circuits may include clock data recovery (CDR) circuitry. The CDR circuitry may receive incoming data and may generate multiple clock signals that are used to latch the incoming data. The CDR circuitry may include data latching circuitry for separately latching even and odd data bits in alternating clock cycles. In particular, the data latching circuitry may be controlled using first, second, third, and fourth clock signals having different respective phase settings. The first and second clock signals may be used to capture even and odd data bits, respectively. The third and fourth clock signals may be used to sample data near the transition between the even and odd data bits. The phase of the first and second clock signals may be dynamically adjusted. The phase setting that yields the optimal link performance may be selected for normal operation.