A three-stage launcher, with solid-propellant first and second stage and a hybridpropellant third stage is considered. The design of the hybrid-propellant upper stage and the whole ascent trajectory are simultaneously optimized by means of a nested direct/indirect procedure, while the characteristics of the first and second stages are assigned. Direct optimization of the parameters that affect the motor design is coupled with indirect trajectory optimization to maximize the launcher payload. A mission profile based on the Vega launcher is considered. The feed system exploits a pressurizing gas, namely helium, with hydrogen peroxide as the oxidizer, and polyethylene as the fuel. The simplest blowdown design is compared with a more complex pressurizing system, which has an additional gas tank that allows for a phase with constant pressure in the oxidizer tank. The optimization provides the optimal values of the main engine design parameters (pressurizing gas mass, nozzle expansion ratio, and initial values of tank pressure, mixture ratio and thrust), the corresponding grain and engine geometry, and the control law (thrust direction during the ascent trajectory and engine ignition and shutoff times). Results show that a hybrid-propellant third stage may be a viable option for small launchers, with improved performance and similar cost compared to an all-solid rocket. The results of the optimization also offer interesting theoretical insight into the problem. Nomenclature A b = burning surface area, m 2 A p = port area, m 2 A th = nozzle throat area, m 2 a = regression constant, m 1+2n kg −n s n−1 C D j = j-th stage drag coefficient C F = thrust coefficient c = effective exhaust velocity, m/s c * = characteristic velocity, m/s D = drag vector, N F = thrust vector, N H = Hamiltonian h = initial port dimension, m L = hybrid stage overall length, m L b = grain length, m m = mass, kg N = number of ports n = mass-flux exponent P = burning perimeter, m p = pressure, bar R g = grain outer radius, m R th = throat radius, m r = position vector, m S j = j-th stage reference area, m 2 t = time, s V = volume, m 3 v = velocity vector, m/s w = web thickness, m x = port angular fraction y = burned distance, m Z = hydraulic resistance, (kg m) −1 α = mixture ratio β = angle (see figure 1), rad γ = specific heat ratio ǫ = nozzle area-ratio * Associateλ r , λ v , λ m = adjoint variables ρ = density, kg/m 3 ω = Earth's angular velocity, rad/s Superscriptṡ = time derivative Subscripts 1 = combustion chamber at head-end a = auxiliary gas atm = atmospheric avg = average BD = beginning of blowdown phase c = combustion chamber at nozzle entrance cc = combustion chamber e = nozzle exit F = fuel g = pressurizing gas gt = pressurizing gas tank hc = hybrid stage casing i = initial value n = nozzle O = oxidizer p = overall propellant (oxidizer + fuel) rel = relative res = residual t = oxidizer tank u = payload vac = vacuum