An infusion device includes a disc-shaped housing that is made from a biocompatible material. The housing contains a reservoir for holding a volume of infusion medium, such as a medication to be administered to the patient. The inlet structure is coupled in flow communication with the reservoir, to allow the reservoir to be filled or refilled. The housing has an outlet through which the infusion medium may be expelled. Any one or combination of aspects may be employed to minimize or reduce the required thickness T of the inlet structure and of the infusion device, including: the selection of a convergence angle of the cone-shaped depression to be within the range of about 60° and 180° and, preferably about 150°; a septum having one or more sealing ribs or a recess for receiving a support ring, to allow the septum to be made relatively thin without compromising sealing or support functions; a cup member having grooves and indentations formed in its inner surfaces, to improve flow of infusion medium without added structural thickness; a valve member having a relatively shallow needle-receiving depression or having a recess for receiving and sharing thickness with a the spring; and an inlet configuration which accommodates a needle having an opening located near its tip and, thus, employs a relatively short stroke of the valve member between closed and open states of the valve member.