The Greener by Design initiative has identified the laminar-flying-wing configuration as the most promising long-term prospect for fuel-efficient civil aviation. However, in the absence of detailed evaluations, its potential remains uncertain. As an initial contribution, this work presents a point design study for a specification chosen to maximize aerodynamic efficiency, via large wingspan and low sweepback. The resulting aircraft carries 220 passengers over a range of 9000 km at Mach 0.67 and has a lift-to-drag ratio of 60.9, far in excess of conventional passenger transports. However, its overall effectiveness is compromised by a high empty-to-payload weight ratio and, because of the huge discrepancy between cruise and climb-out thrust requirements, a poor engine efficiency. As a result, it has a much less marked fuel-consumption advantage (11.4–13.9 g per passenger kilometer, compared to 14.6) over a conventional competitor designed, using the same methods, for the same mission. Both weight ratio and engine efficiency could be improved by reducing aspect ratio, but at the cost of an aerodynamic efficiency penalty. This conflict, which has not previously been recognized, is inherent to the laminar-flying-wing concept and may undermine its attractiveness.