A machine (10) for machining workpieces with optical quality has at least one workpiece spindle (12), which rotatably drives a workpiece (L) to be machines about a workpiece axis of rotation (C). A swivel head (14) located opposite the workpiece spindle, is pivotable about a pivot axis (B), and bears at least two tool spindles (16, 18), each of which rotatably driving at least one machining tool (T1, T2, T3) about a tool axis of rotation (D, D′). The workpiece spindle and the swivel head (14) are adjustable relative to one another along three mutually perpendicular linear axes (X, Y, Z). One axis (Y) extends parallel to the pivot axis (B). Another axis (Z) extends parallel to the axis (C) of workpiece rotation. At least one tool spindle is attached to the swivel head with its tool axis of rotation (D′) extending parallel to the pivot axis (B).