Gas-free calibration is an appealing new alternative for calibrated fMRI. Using simulations, we determined that estimates of the calibration parameter, M, obtained directly by estimating R2’ with asymmetric spin echo imaging, are negatively biased. This is due to imperfect spin echo refocusing of spins diffusing in the extravascular space. When we modelled the spin echo attenuation as a quadratic-exponential decay, the imperfect refocusing effects were accurately accounted for over intermediate to large vessel sizes. When tested in vivo, increases in M were observed when using the quadratic model, however, additional sources of decay also contributed to M.