In preon models based on chiral gauge theories, we show that light composite fermions can ensue as a result of gauging a subset of preons in a vector-like manner. After demonstrating how this mechanism works in a toy example, we construct a one generation model of quarks which admits a hierarchy between the up and down quark masses as well as between these masses and the compositeness scale. In simple extensions of this model to more generations we discuss the challenges of obtaining any quark mixing. Some possible phenomenological implications of scenarios where quarks and leptons which are heavier are also less pointlike are also considered.

22 pages, 2 figures not included, latex, UCLA/92/TEP/49