Entangled probes provide a significant precision gain over classical strategies for noiseless parameter estimation. However, recent results seem to indicate that any small amount of realistic noise restricts the advantage of quantum strategies to an improvement by at most a multiplicative constant. We identify a relevant scenario in which one can overcome this restriction and attain super-classical precision scaling even in the presence of uncorrelated noise. The quantum improvement can be significantly enlarged when the noise is concentrated along some spatial direction, while the Hamiltonian governing the evolution which depends on the parameter to be estimated can be engineered to point along a different direction. In the case of perpendicular orientation, scaling is super-classical, and we can identify a state which achieves the optimum.