Persistent scatterer interferometry (PSI) techniques using amplitude analysis and considering a temporal deformation model for PS pixel selection are unable to identify PS pixels in rural areas lacking human-made structures. In contrast, high rates of land subsidence lead to significant phase-unwrapping errors in a recently developed PSI algorithm (StaMPS) that applies phase stability and amplitude analysis to select the PS pixels in rural areas. The objective of this paper is to present an enhanced algorithm based on PSI to estimate the deformation rate in rural areas undergoing high and nearly constant rates of deformation. The proposed approach integrates the strengths of all of the existing PSI algorithms in PS pixel selection and phase unwrapping. PS pixels are first selected based on the amplitude information and phase-stability estimation as performed in StaMPS. The phase-unwrapping step, including the deformation rate and phase-ambiguity estimation, is then performed using least-squares ambiguity decorrelation adjustment (LAMBDA). The atmospheric phase screen (APS) and nonlinear deformation contribution to the phase are estimated by applying a high-pass temporal filter to the residuals derived from the LAMBDA method. The final deformation rate and the ambiguity parameter are re-estimated after subtracting the APS and the nonlinear deformation from that of the initial phase. The proposed method is applied to 22 ENVISAT ASAR images of southwestern Tehran basin captured between 2003 and 2008. A quantitative comparison with the results obtained with leveling and GPS measurements demonstrates the significant improvement of the PSI technique.