Connecting structures for integrated circuit chips or dice are fabricated by forming a plurality of sets of leads on a first surface of a flexible tape. The sets of leads penetrate through to the second surface of the tape at ends of the leads, via holes formed in the tape. Small contacts are formed to extend beyond the second surface of the tape at the points where the leads penetrate through the tape. The contacts formed at a first end of each of the leads are arranged in a pattern which aligns with corresponding contacts on the integrated circuit chip. The chips are then bonded to the contacts formed at the first ends of the leads, and the chips are subsequently enclosed by a suitable encapsulant such as epoxy. The contacts formed at second ends of the leads are arranged in a pattern which is larger than the pattern of contacts at the first end of the leads, and are disposed for connection to external circuitry.