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Modern aircraft, particularly fighters, are characterized by a high degree of geometrical complexity. In transonic computations about such configurations, small disturbance (TSP) formulations on Cartesian grids offer a robust and cost-effective alternative to more elaborate methods in many engineering applications. Wing boundary conditions are then easily imposed using thin-wing theory, whereas fuselage boundary conditions usually are more difficult to implement. This paper presents a numerical method for solving the TSP equation about a complex slender configuration emphasizing a consistent treatment of the boundary conditions on the fuselage surface. The basic concept is a decomposition into two coupled inner and outer problems, using the theory of matched asymptotic expansions as guidance. The outer problem is discretized using a standard three-dimensional finite-difference scheme. The inner problem, enforcing the fuselage boundary conditions, is solved as a sequence of crossflow problems, using a linear two-dimensional panel method. Several test runs on a CRAY-1 computer have demonstrated the reliability and robustness of the above procedure. Computed pressure distributions for a number of three-dimensional cases, including one of the fighter type, are in good agreement with wind tunnel test data.