I will present a construction of a singular measure on three dimensional sphere $S^3$ whose non-zero components in spherical harmonic decomposition are concentrated around lines $y=ax$ and $x=ay$. This could be seen as a generalization of Aleksandrov's singular pluriharmonic measure or an inverse to the Brummelhuis condition of absolute continuity. The main ingredient is a construction of bounded spherical harmonics with small, localized Fourier spectra. Joint work with M. Wojciechowski.