A one-dimensional model is proposed to predict the leveling of coating defects or irregularities on a planar surface. Though shear thinning rheology is the focus of this paper, any viscous non-Newtonian rheology can be included in the model. Surface tension, gravity and viscous forces are accounted for in the model. A novel numerical technique is presented to obtain solutions of the model. Results agree with a full two-dimensional solution of the flow held obtained with a spectral element method. A new dimensionless group is identified which indicates the significance of shear-thinning theology. Defects are made with a notched blade used to coat pigmented liquids on polymer films. The defect shapes are obtained at different times by drying under infrared. The dried surface is characterized with a stylus profilometer. The surface profiles and the final amount of leveling compare well with the model predictions.