Many engineering and scientific numerical simulations require solving extremely ill-conditioned linear systems. This ill-conditioning is often driven by highly anisotropic meshes, high-order finite element discretisations, or, most severely, their combination. It is routinely encountered, for instance, in boundary-layer-resolving CFD meshes, in slender and layered composite-structure models that demand through-thickness refinement, and in magnetically confined fusion plasma simulations with strong field-aligned anisotropy. Even with iterative solvers and state-of-the-art multilevel preconditioners, convergence can stall for thousands of iterations, sometimes on relatively small benchmark problems . Direct solvers are therefore frequently adopted for robustness, but their computational and memory costs scale poorly, limiting their practicality for routine large-scale industrial applications. In such settings, iterative solvers become practical only when equipped with physics-informed preconditioners that leverage the dominant anisotropy directions to reduce the condition number. A prominent example is the Linelet preconditioner , which factorises the restriction of the operator along node lines aligned with the anisotropy direction and can substantially improve conditioning. In this work, we present a comprehensive study of how Linelet preconditioning effectively reduces the condition number of a system through the analysis of a controlled model problem. We investigate the spectral properties of the preconditioned operator and demonstrate how this technique can be extended to problems assembled over high-order meshes. By generalizing the line-construction algorithms to accommodate higher-degree basis functions, we show that it is possible to recover robust convergence rates even in the presence of extreme anisotropy.