A multi-chip module (MCM-10) includes a substrate (11), one or more photonic chips (14) disposed on the substrate, and an electronic chip (12) disposed on the substrate. The one or more photonic chips include one or more optical channels (22), which are configured to guide propagating optical signals, and two or more photonic modulator-segments (18) coupled to each of the optical channels, each photonic modulator-segment configured to modulate the propagating optical signals responsively to digitally modulated driving electrical signals provided thereto. The electronic chip is configured to generate the digitally modulated driving electrical signals on multiple different lanes (16) of the electronic chip, synchronize the driving electrical signals on the multiple lanes to a same clock, separately control respective phases of the driving electrical signals, fine-tune the voltages of the driving electrical signals on the multiple lanes, and drive the photonic modulator-segments on the photonic chips with the synchronized and phase-controlled driving electrical signals.