The present invention relates to a machine for preparing coffee infusions by means of a liquid under pressure, in particular water under pressure, the machine comprising: a pump assembly (11) arranged to raise the pressure of the liquid outgoing from the pump assembly up to a preset pressure value (PI); one or more dispensing units (14) connected to the pump assembly, each dispensing unit (14) being arranged to dispense the coffee infusion; one or more pressure managing devices (20), each managing device (20) being connected to a certain dispensing unit (14). In the machine (10), the pressure managing device (20) includes a first duct (15) and at least one second duct (16) that are connected in parallel, have a common outlet and are arranged to supply the dispensing unit (14), during the coffee infusion preparation, with liquid at different pressures. The invention further concerns the pressure managing device (20) and a method of preparing the coffee infusion, including dynamically modifying the pressure during the infusion preparation.