A new class of compact schemes are derived that obtain high-order accuracy while using a very small stencil size. These schemes are shown to be equivalent to standard high-order compact schemes. These new schemes reduce the computational effort while offering easier boundary stencil specification than the existing schemes. Results are shown for linear and nonlinear 1-D benchmark problems and a 2-D linear benchmark problem. Boundary stencils and boundary condition specification are described and demonstrated. Introduction The field of computational aeroacoustics is focused on obtaining long-term, time-accurate numerical solutions to unsteady flow and acoustic problems. In order to accomplish this, a high-accuracy time-marching scheme is combined with high-resolution spatial derivatives. There are two main classes of high-accuracy finite-difference schemes: explicit schemes and compact schemes (e.g., Refs. [1-10]). Explicit schemes employ large computational stencils for accuracy, while compact schemes use smaller stencils by solving for the spatial derivatives as independent variables at each grid point. While compact schemes are more accurate than the equivalent explicit scheme, they have two disadvantages: first, a matrix must be inverted to obtain the spatial derivative at a point; second, the boundary stencil has a large effect on the stability and accuracy of the scheme. Recently, a new class of high-accuracy compact MacCormack-type schemes have been derived for computational aeroacoustics. Following this development, a new class of high-order compact schemes are derived which use three-point stencils and return up to eighth-order accuracy. This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States. 1 $. Senior Research Associate, Member AIAA. Description of Compact Schemes A general compact derivative of a function f may be written as: