The present work demonstrates a fast and improved technique for dewarping nonlinearly warped document images. The images are first dewarped at the page-level by estimating optimum inverse projections using curvilinear homography. The quality of the process is then estimated by evaluating a set of metrics related to the characteristics of the text lines and rectilinear objects for measuring parallelism, orthogonality, etc. These are designed specifically to estimate the quality of the dewarping process without the need of any ground truth. If the quality is estimated to be unsatisfactory, the page-level dewarping process is repeated with finer approximations. This is followed by a line-level dewarping process that makes granular corrections to the warps in individual text-lines. The methodology has been tested on the CBDAR 2007 / IUPR 2011 document image dewarping dataset and is seen to yield the best OCR accuracy in the shortest amount of time, till date. The usefulness of the methodology has also been evaluated on the DocUNet 2018 dataset with some minor tweaks, and is seen to produce comparable results.