It is common for new aircraft configuration proposals to include some kind of lifting body. The reduction in fuselage–wing interference drag, in principle, improves span efficiency and hence allows for reduction in total span and structural weight. One such proposal involves controlling body circulation by a central trailing-edge flap, and though the basic idea has been supported in initial wind tunnel tests, there have been no further attempts to systematically explore the design space for these wing–body–tail geometries. The first purpose of this study was to numerically simulate the experimental work. Simulations with incompressible Reynolds-averaged Navier–Stokes equations show quite significant separation over the aftbody, limiting the effectiveness of the trailing edge. The second purpose of the paper was to investigate the characteristics when two low-drag bodies from literature were used in otherwise similar wing–body–tail configurations. The wing–body–tail assemblages had different aftbody separation characteristics. Adding the trailing edge increased the total drag coefficient, and the expected improvement of induced drag did not lead to a net benefit. It is concluded that, if such a favourable geometry exists, then it has not been found here.