A major obstacle to the understanding of gradient-driven transport systems has been their apparently wide kinetic diversity, which has seemed to require a variety of ad hoc mechanisms. Ordinary kinetic analysis, however, has been hampered by one mathematically powerful but physically dubious assumption: that rate limitation occurs in transmembrane transit, so that ligand-binding reactions are at equilibrium. Simple models lacking that assumption turn out to be highly flexible and are able to describe most of the observed kinetic diversity in co- and counter-transport systems. Our "minimal" model of cotransport consists of a single transport loop linking six discrete states of a carrier-type molecule. The state transitions include one transmembrane charge-transport step, and one step each for binding of substrate and cosubstrate (driver ion) at each side of the membrane. The properties of this model are developed by sequential use of realistic experimental simplifications and generalized numerical computations, focussed to create known effects of substrate, driver ion, and membrane potential upon the apparent Michaelis parameters (Jmax, Km) of isotopic substrate influx. Specific behavior of the minimal model depends upon the arrangement of magnitudes of individual reaction constants among the whole set (12) in the loop. Well defined arrangements have been found which permit either increasing membrane potential or increasing external driver-ion selectively to reduce the substrate Km, elevate Jmax, jointly raise both Km and Jmax, or lower Km while raising Jmax. Other arrangements allow rising internal driver ion to act like either a competitive or a noncompetitive inhibitor of entry, or allow internal substrate to shut down ("transinhibit") influx despite large inward driving forces. These findings obviate most postulates of special mechanisms in cotransport: e.g., stoichiometry changes, ion wells, carrier-mediated leakage, and gating - at least as explanations for existing transport kinetic data. They also provide a simple interpretation of certain kinds of homeostatic regulation, and lead to speculation that the observed diversity in cotransport kinetics reflects control-related selection of reaction rate constants, rather than fundamental differences of mechanism.