The alternative formulated in the title has a chance to be settled, when the existence of the LSND effect is experimentally excluded or confirmed. The first option, much discussed in literature, works in the case of three active neutrinos \nu _e \nu _\mu   \nu _\tau , when among their massive states \nu ₁ \nu ₂ \nu ₃ there is no direct mixing between \nu ₁ and \nu ₃ , and the mass hierarchy m²₁ \lesssim m²₂  \ll m²₃ holds. This option is consistent with the observed deficits of solar \nu _e's and atmospheric \nu _\mu 's,  if \Delta m²₂₁ \leftrightarrow \Delta m²_sol and \Delta m²₃₂ \leftrightarrow \Delta m²_atm . On the other hand, the second option is an extension of the idea of the former to the case of four neutrinos \nu _s , \nu _e , \nu _\mu  , \nu _\tau (including one sterile neutrino \nu _s ), when among their massive states \nu ₀ , \nu ₁ ,  \nu ₂ , \nu ₃ there are no direct mixings between \nu ₀ and \nu ₂ , \nu ₀ and \nu ₃ , \nu ₁ and \nu ₃ , and the mass hierarchy m²₀\lesssim m²₁ \ll m²₂ \lesssim m²₃ is now valid. Such an option, belonging to a class of textures widely discussed in literature, may be consistent with the observed deficits of solar \nu _e 's and atmospheric \nu _\mu 's as well as with the LSND appearance of \nu _e 's in the beam of accelerator \nu _\mu 's, if now \Delta m²₁₀ \leftrightarrow \Delta m²_sol , \Delta m²₃₂ \leftrightarrow \Delta m²_atm and \Delta m²₂₁ \leftrightarrow \Delta m²_LSND (however, in the case of solar \nu _e 's the role of \nu _s 's in the disappearance of \nu _e 's is recently questioned). In both options, only the close neighbours in the hierarchies of massive neutrinos \nu ₁ , \nu ₂ , \nu ₃ and \nu ₀, \nu ₁, \nu , \nu ₃, respectively, mix directly}. This characteristic feature of the two-mixing texture for three neutrinos or the three-mixing texture for four neutrinos may be somehow physically significant.

PACS numbers: 12.15.Ff, 14.60.Pq, 12.15.Hh