Signal-alignment circuitry, comprising: phase-rotation circuitry connected to receive one or more input clock signals and operable to generate therefrom one or more output clock signals; and control circuitry operable to control the amount of phase rotation applied by the phase-rotation circuitry to carry out a plurality of alignment operations, the alignment operations comprising: one or more first operations each comprising rotating one or more of said output clock signals relative to one or more of the other said output clock signals, to bring a phase relationship between said output clock signals, or clock signals derived therefrom, towards or into a given phase relationship; and one or more second operations each comprising rotating all of said output clock signals together, to bring a phase relationship between said output or derived clock signals and said input clock signals or an external-reference signal towards or into a given phase relationship.