A simple but accurate regression method for reducing the conventional single-frame interferograms that primarily arise in flow and heat-transfer measurements is proposed and tested. Phase extraction from the nonlinear interferogram intensity model becomes an ill-posed nonuniqueness problem. Unlike previous regression techniques, the method is based on iterative independent estimation of the individual terms appearing in the model to resolve this problem. Testing demonstrates stable convergence under a wide range of fringe numbers and noise levels. In comparison with the Fourier transform method the regression method provides enhanced accuracy, especially for cases involving few fringes, opaque boundaries, and phase discontinuities. It also allows direct gradient calculation. These features are very attractive for flow measurements despite its slow processing time.