Crude oil fouling on heat transfer surfaces is often described as the result of two competing mechanisms: a deposition and a deposition-offsetting mechanism. There is uncertainty about whether the offsetting mechanism is suppression (due inhibition of attachment or back-diffusion of foulant from near the wall into the bulk) or removal of foulant already deposited, due to (i) difficulties in experimentally identifying and isolating the key phenomena and (ii) the cumulative measurement of deposition rates by monitoring thermal exchange rates (or resistance) alone. Here, the question is addressed of whether it is conceptually possible to distinguish such phenomena, and if so, in which conditions. A recently developed two-dimensional (2D) deposit model and a thermohydraulic model of a heat exchanger tube are used to assess the system response to removal, suppression, aging, and consolidation (for which a new model is proposed). It is shown that while suppression or removal lead to undistinguishable behavior during overall deposit growth, thermal and hydraulic responses will differ in certain conditions, for which an experimental procedure is suggested. Simultaneous consideration of thermal and hydraulic effects and accurate characterization of the deposit aging and consolidation processes are suggested as a way to allow the unambiguous identification of the dominant deposition-offsetting mechanism.