An extensive on-line nuclear orientation study of the angular distribution
in favoured alpha -decay of Bi, At and Rn nuclei near the Z=82 and N=126 sh
ell closures, performed at ISOLDE is presented. Surprisingly large alpha an
isotropies were observed, showing systematic changes from one isotope to th
e next. Comparison with various theoretical models proves that anisotropic
alpha -emission in favoured decays of near-spherical nuclei is determined b
y the structure of the decaying nucleus.