A method for determining a spacecraft orbit solely from Doppler data is described. After removing known components from the Doppler signature, the portion of the signature due only to the spacecraft motion relative to the central body is parameterized. A Newton-Raphson method is applied to obtain the solution. Parameters which yield a nearly diagonally dominant partials matrix are defined. A wide range of convergence is demonstrated for data from the Magellan orbiter around Venus and for simulated data from the NEAR (Near Earth Asteroid Rendezvous) mission. This new method is particularly important for orbits around asteroids and comets, where a velocity error of only a few meters per second can place the spacecraft in an entirely unknown orbit.