We show experimental results demonstrating the feasibility of an extremely fast sequential phase-diversity (SPD) algorithm for point sources. The algorithm can be implemented on a typical adaptive optics (AO) system to improve the wavefront reconstruction beyond the capabilities of a wavefront sensor by using the information from the imaging camera. The algorithm is based on a small-phase approximation enabling fast numerical implementation, and it finds the optimal wavefront correction by iteratively updating the deformable mirror. Our experiments were made at an AO-setup with a 37 actuator membrane mirror, and the results show that the algorithm finds an optimal image quality in 5-10 iterations, when the initial wavefront errors are typical non-common path aberrations having a magnitude of 1-1.5 rad rms. The results are in excellent agreement with corresponding numerical simulations.