||This paper proposes a gradient-based progressive optimization technique, which can be efficiently combined with black-box simulation codes. Its efficiency relies on the simultaneous convergence of the flow solution, of the gradient evaluation, and of the design update, as well as on the use of progressively finer grids. The developed numerical technique has general validity and is here applied to the fluid-dynamic design optimization of the intake of a small-size turbojet engine, at high load and zero flight speed. Two simplified design criteria are proposed, which avoid simulating the flow in any turbojet components other than the intake itself. Using a geometrically constrained polynomial profile, both design optimizations have been produced in less than the amount of computational work to perform nine flow analyses; moreover, both optimizations have provided almost coincident intake profiles. Negligible performance improvements have been obtained by removing one geometrical constraint, at the price of almost tripling the CPU time required. Finally, the original and the optimal profiles have been mounted on the same small-scale turbojet engine and experimentally tested, to assess the resulting improvements in terms of overall performances. All numerical and experimental achievements can be extended to the intake of a microturbine for electricity generation.