A connector uses a plurality of individual terminal assemblies to form a high-density connector. The terminal assemblies all have insulative body portions that support arrays of signal terminals and ground terminals or ground members. The terminals all have their own associated body portions which are supported by the insulative body portions and contact portions that extend out from a front, or mating face, of the assemblies. The terminal contact portions and include flexing portions formed therewith which are disposed between the terminal body and contact portions. The terminals further include insulative support members that are applied to the terminals and which serve to define the contact and flexing portions of the terminals. The support members are fixed within a carrier, such as a shroud member, which is not attached to any one portion of the connector. The support members permit the terminals and shroud to move as a single unit and flex in different directions, relative to the insulative body portions that support the terminals.