For a Neoclassical growth model, exponential discounting is observationally equivalent to quasi-hyperbolic discounting, if the instantaneous discount rate decreases asymptotically towards a positive value (Barro 1999). Conversely, in this paper a zero long-run value allows a solution without stagnation. New patterns of growth, specifically a less than exponential but unbounded growth can be attained, even without technological progress. The growth rate of consumption decreases asymptotically towards zero, although so slowly that consumption grows unboundedly. The asymptotic convergence towards a non-hyperbolic steady-state which saving rate matches the intertemporal elasticity of substitution and the speed of convergence towards this equilibrium are analyzed.