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A new family of hierarchical divergence-conforming vector bases is proposed for tetrahedral, prism and brick cells. These functions span the divergence-conforming reduced-curl spaces of Nédélec. The bases are constructed from orthogonal scalar polynomials to enhance their linear independence, which is a simpler process than an orthogonalization applied to the final vector functions. Specific functions are tabulated to order 6.5. These basis are intended for use with numerical solutions of volume integral equations or differential equations containing divergence operators.