Basis sets featuring single-exponent radial functions for each of the n subshells and orthogonality of the radial parts for dierent values of n within the same have been generated for elements 1 to 54 of the Periodic Table, by minimizing the total energy for dierent spectroscopic states. The derived basis sets can be fairly dubbed as MAP (minimal atomic parameter / Moscow-Aachen-Paris) basis sets. We show that fundamental properties (total energy, radial expectation values, node positions, etc.) of the generated MAP orbital sets are astonishingly close to those obtained with much larger basis sets known in the literature, without numerical inconsistencies. The obtained exponents follow simple relations with respect to the nuclear charge Z. Possible further applications, trends, and limitations are discussed.