Recursive equations for the efficient computation of nearly orthogonal, C 0 continuous p-version approximation functions ("max-orthogonal") are developed in one dimension and used to construct hexagonal ("brick") element approximation functions. A modification to the functions is presented to simplify adaptive p-refinement, resulting in "semi-orthogonal" approximation functions. These functions are found to produce Laplace equation stiffness matrices, as well as mass matrices, with substantially lower condition numbers compared to standard Legendre-based modal functions. Sample problems are presented using a conjugate gradient matrix solver to compare the matrix solution computation times using max-orthogonal, semi-orthogonal, and standard modal functions.Automatic adaptive polynomial refinement is also discussed and applied to these sample problems. The semi-orthogonal functions are found to be an efficient and practical means of achieving very well-conditioned p-version finite element matrices.