In this paper, an immersed-boundary method developed for compressible viscous flows is further improved to account for better mass conservation and address numerical instabilities associated with the velocity reconstruction. The 2D embedded object is represented as a set of line segments along with their outward unit normal vectors. A forcing method that leverages the finite-volume approach is used, wherein the solution at cell interface that lie near the boundaries of the embedded solid is reconstructed. A cut-cell type approach is proposed to the determine the effective flow through area of a cell face that is intersected by the immersed boundary to improve mass conservation; however, the boundary of the embedded object is not reconstructed in its entirety. This method shall is validated for supersonic inviscid flow past a bump in a channel and a circular cylinder, transonic viscous flow past a NACA0012 airfoil and supersonic viscous flow past a circular cylinder. The results are compared with simulations from literature using contours of flow properties, surface pressure and show fair to good agreement. © 2021, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.