The development of the compressible flow tables by Shapiro, Hawthorne and Edelman [1-3] was a boon to the one-dimensional modeling of compressible flows - isentropic flow, Fanno flow, Rayleigh flow, normal shock. Nevertheless, the use of the tables is cumbersome. Furthermore, becoming engrossed with the mechanics of applying the tables, students and practitioners often lose sight of the fundamentals that are being applied. The present paper will illustrate the direct application of the basic one-dimensional governing equations to the modeling of compressible flows. In a straightforward fashion mass, momentum, energy and entropy balances, along with transport and property relations, are applied directly (without the use of tables or graphs) to model and to find solutions. Moreover, unlike the tables, the modeling does not need to assume ideal gases, let alone a constant ratio of specific heats. The key to this improved and easy approach, unavailable at the time the tables were developed, is the accessibility of equation solving software that includes property relations for gases and liquids. In particular, in the present work, EES (from fchart software; see fchart.com) was employed.