Circuitry for use in aligning bytes in a serial data signal (e.g., with deserializer circuitry that operates in part in response to a byte rate clock signal) includes a multistage shift register for shifting the serial data signal through a number of stages at least equal to (and in many cases, preferably more than) the number of bits in a byte. The output signal of any shift register stage can be selected as the output of this “bit slipping” circuitry so that any number of bits over a fairly wide range can be “slipped” to produce or help produce appropriately aligned bytes. The disclosed bit slipping circuitry is alternatively or additionally usable in helping to align (“deskew”) two or more serial data signals that are received via separate communication channels.