Model-Free Inversion-based Iterative Control (MFIIC) enables tracking performance improvement of systems that perform repeating tasks without using a model of the system. The aim of this paper is (i) to show that MFIIC can result in a severe loss of performance if the Signal-to-Disturbance-Ratio (SDR) approaches 1, and (ii) to propose a solution to this problem. The Smoothed MFIIC (SMFIIC) method is developed, which does not suffer from the undesirable learning transient behavior. This is achieved by adaptively regulating the learning speed to ensure smooth convergence. The existence of bad learning transients in MFIIC and the efficacy of SMFIIC are illustrated on an experimental desktop printer.