Inertial confinement fusion (ICF) experiments at the National Ignition Facility (NIF) use high-density carbon shells doped with low-concentration tungsten in a thin, uniform-density, buried layer, to suppress deleterious high-energy x-ray pre-heating. Recent radiation-hydrodynamics simulations suggest that this boxcar dopant-concentration profile causes hydrodynamically unstable density gradients leading to fuel-shell mixing and up to 2× degraded neutron yields. To address this, a new ramped profile was tested, where the dopant concentration linearly ramps up and back down. Two NIF experiments using this strategy demonstrated neutron yield improvements of up to 2.2× over the closest boxcar comparison, achieving a record 8.6 MJ yield, 20.1 keV hot-spot temperature, and a target gain of 4.1. These results show that ramped doping is consistent with mitigation of fuel-ablator mixing and marks a key development for ICF science.