In boundary element method applications there are contradicting requirements which need to be accommodated skillfully in order to achieve high accuracy and high speed at the same time. Regarding acceleration of computations, it is desirable, besides parallelization and other conventional measures, to extract costly “universal” features from the computations which are common to a certain class of problems. If successful the resulting Universal Functions (UFs) can be pre-calculated and stored and referred to whenever necessary. As can be shown the intro- duction of UFs, however, requires additive factorization of terms, leading to high-order algebraic singularity in infrared region in spectral domain (zero and small values of the wavenumbers). Thereby, the algebraic order of the additional singularity depends on the degree of smoothness of the basis- and testing functions employed — the smoother the basis and testing functions the higher the order of singularity at the origin of the coordinate system in the spectral domain. On the other hand smooth basis- and weighting functions improve the convergence of the in- volved Fourier-type integrals algebraically in ultraviolet region (large values of the wavenumber in spectral domain). The main result in this contribution is the fact that all the aforementioned seemingly contradicting requirements can be reconciled naturally. The magic is done by recog- nizing that Hadamard Finite Parts appear in the introduced Universal Functions automatically, with one additional pleasant surprise: Ordinarily Hadamard Finite Parts technique, as the name implies, considers finite parts of infinite integrals, thus throwing away the infinities in the cal- culations. In the proposed procedure the infinities add up to zero exactly. Finally it should be pointed out that the Hadamard Finite Parts in the UFs are exclusively induced by the chosen basis- and testing functions, thus, justifying the using of the “self-induced” property in the title.