The EIT reconstruction problem is approached as an optimization problem where the difference between a simulated impedance domain and the observed one is minimized. This optimization problem is often solved by Simulated Annealing (SA), but at a large computational cost due to the expensive evaluation process of the objective function. We propose here, a variation of SA applied to EIT where the objective function is evaluated only partially, while ensuring upper boundaries on the deviation on the behavior of the modified SA. The reconstruction method is evaluated with simulated and experimental data.