Fluorescence recovery after photobleaching (FRAP) carried out on a confocal laser-scanning microscope (CLSM) performs well for photobleached disks that are large compared to the resolution of the bleaching beam. For smaller disks approaching this resolution, current FRAP models providing a closed-form solution do not allow one to extract the diffusion coefficient accurately. The new generalized disk model we present addresses this shortcoming by bringing into account the bleaching resolution and the total confocal imaging resolution. A closed-form solution is obtained under the assumption of linear photobleaching. Furthermore, simultaneous analysis of FRAP data collected at various disk sizes allows for the intrinsic determination of the instrumental resolution parameters, thereby obviating the need for an extrinsic calibration. A new method to estimate the variance of FRAP data is introduced to allow for proper weighting in this global analysis approach by nonlinear least squares. Experiments are performed on two independent CLSMs on homogeneous samples providing validation over a large range of diffusion coefficients.