A clock generating circuit is operated in a phase-locking mode to generate an output clock signal having a first frequency that is phased-locked with respect to a variable-frequency input clock signal. After a frequency transition in the input clock signal, phase-locking is disabled within the clock generating circuit to transition the output clock signal from the first frequency to a second frequency that lacks phase-alignment with the input clock signal, then a frequency-lock range of the clock generating circuit is adjusted to transition the output clock signal from the second frequency to a third frequency that also lacks phase alignment with the input clock signal. After adjusting the frequency-lock range of the clock generating circuit, phase-locking is re-enabled therein to transition the output clock signal from the third frequency to a fourth frequency that is phase-aligned with the variable-frequency input clock signal.