We study the boundary between the vortex-solid and the vortex-liquid phases in the Hc–Hab plane, for irradiated Bi2Sr2CaCu2O8+δ single crystals, by measuring the ac-local magnetic permeability in tilted magnetic fields. For high temperatures and at the phase boundary, we find that the c-axis magnetic field component Hctrans decreases linearly when increasing the in-plane magnetic field Hab, surprisingly in a wider angular range than in pristine samples. Strikingly, at lower temperatures, this linear decrease of Hctrans(Hab) transforms to a concave, hyperbolic-like, curve that differs even more strongly from the usual Ginzburg–Landau (GL) elliptical phase boundary. We also propose a theoretical approach to solve this puzzle. Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/49054/2/njp6_10_226.pdf