•I have revised the manuscript “Spectral methods for capillary surfaces described by bounded generating curves” and submit these changes for consideration for publication.•I have substantially replaces the code snippets with a flowchart and I have added clear and detailed summaries of the goals of each table, as indicated was desired by the referee. We consider capillary surfaces that are constructed by bounded generating curves. This class of surfaces includes radially symmetric and lower dimensional fluid-fluid interfaces. We use the arc-length representation of the differential equations for these surfaces to allow for vertical points and inflection points along the generating curve. These considerations admit fluids in capillary tubes, sessile drops, and fluids in annular tubes as well as other examples. We present a pseudo-spectral method for approximating solutions of the associated boundary value problems based on interpolation by Chebyshev polynomials. This method is observably more stable than the traditional shooting method and it is computationally lean and fast. The algorithm is also adaptive, but does not use the adaptive automation in Chebfun.