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The formulation of a model that can reliably simulate the temporal groundwater level fluctuations of an aquifer is important for effective water resource management and for the prevention of possible desertification effects. Mires Basin at the island of Crete, Greece, is part of a major watershed with significantly reduced groundwater resources because of overexploitation during the past 30 years. In this work, the interannual variability of groundwater level is modeled with a discrete time autoregressive exogenous variable (ARX) model that is based on physical grounds (soil-water balance equation). Precipitation surplus is used as an exogenous variable in the ARX model. Three new modified versions of the original form of the ARX model are proposed and investigated: the first considers a larger time scale; the second considers a larger time delay in terms of the groundwater level input; and the third considers the groundwater level difference between the last two hydrological years, which is incorporated in the model as a third input variable. Modeling results for the time series of the spatially averaged groundwater level show very good agreement, after an initial adaptation period, with measured data. Among the three modified versions of the original ARX model considered in this work, the third model version shows significantly better agreement with measured data.