A catheter with basket-shaped electrode assembly with spines configured forhyper-flexingin a predetermined, predictable manner when a compressive force acts on theassembly from eitherits distal end or its proximal end. At least one spine has at least one regionof greater (or hyper)flexibility that allows the electrode assembly to deform, for example,compress, for absorbing anddampening excessive force that may otherwise cause damage or injury to tissuewall in contactwith the assembly, without compromising the structure and stiffness of theremaining regions of thespine, including its distal and proximal regions. The one or more regions ofgreater flexibility inthe spine allow the spine to flex into a generally V-shape configuration or agenerally U-shapeconfiguration.