It is known that some (BEDT-TTF) 2 X layered organic superconductors undergo a glassy transition near 80 K. Our purpose is to exploit quenched disorder to get new insights on both the superconducting state (T ≤ 12 K) and the glassy transition by studying the superconducting properties as functions of annealing time (t a ) and temperature (T a 1) The data can be described by a percolation cluster model. 2) At short time scales, the clusters grow with t a following a power law. 3) At large time scales the clusters grow toward a thermodynamic state following a stretched exponential law However, we emphasize that the low-temperature state contains some amount of quenched disorder that strongly depends on the anion, the applied pressure, the cooling conditions and, more importantly, on whether the ethylene groups are formed by hydrogen bonds (denoted H8-Br) or deuterium bonds (denoted D8-Br). This is why the exact nature of the 80 K anomaly and the associated low-temperature superconducting state are still not understood.)As a matter of fact, D8-Br exhibits several puzzling superconducting properties. Some of these properties were ascribed to the appearance of a magnetic transition at low temperature (10-20 K), the meaning of which is unclear: Several mechanisms have been proposed including spin-density waves 13 , spin canting 12 , or the suppression of superconductivity by dispersed magnetic ions associated with the persistent disorder 14 . Also, some authors 7,8 3 ascribed the decrease of the apparent superconducting volume to an increase in λ (the inplane penetration depth) through mean-free-path effect 7 .However none of these mechanisms is able to explain, even qualitatively, the following experimental facts: 1) The fact that the apparent magnetic critical current density j c (as deduced from the Bean model) always decreases as the degree of quenched disorder increases.2) The low-field susceptibility also decreases in the same experimental conditions.To account for such a decrease, one is led to assume that λ can reach unphysical values, as high as 0.1 mm [8] (and much more if applied to the present results). 3) Despite these large changes in the apparent j c and λ , T c stays almost constant. 4) As the quenched disorder is increased; one observes: firstly, the appearance of increasing irreversibilities at H << H c1 (for instance, H = 0.1 Oe and T = 2 K), secondly, a large broadening of the superconducting transition.One of the purposes of this work is to prove that all of these features can naturally be explained in the framework of a granular model and the associated weak links connecting the grains.We have investigated the ac magnetic susceptibility and the dc magnetization of the superconducting phase after performing a series of thermal treatments on a D8-Br singlecrystal of dimension ~ 1 × 1 × 0.25 mm 3 . To this end, we annealed the sample inside the SQUID cryostat at different fixed temperatures T a ranging from 65 to 110 K. Moreover, in order to carefully monitor the development of ethylene or...