Stimulated emission depletion (STED) fluorescence microscopy squeezes an excited spot well below the wavelength scale using a doughnut-shaped depletion beam. To generate a doughnut, a scale-free vortex phase modulation (2D-STED) is often used because it provides maximal transverse confinement and radial-aberration immunity (RAI) to the central dip. However, RAI also means blindness to a defocus term, making the axial origin of fluorescence photons uncertain within the wavelength scale provided by the confocal detection pinhole. Here, to reduce the uncertainty, we perturb the 2D-STED phase mask so as to change the sign of the axial concavity near focus, creating a dilated dip. By providing laser depletion power, the dip can be compressed back in three dimensions to retrieve lateral resolution, now at a significantly higher contrast. We test this coherent-hybrid STED (CH-STED) mode in x-y imaging of complex biological structures, such as the dividing cell. The proposed strategy creates an orthogonal direction in the STED parametric space that uniquely allows independent tuning of resolution and contrast using a single depletion beam in a conventional (circular polarization-based) STED setup.