  This paper is a follow-up on two previous ones, in which properties of
blueshifted rays were investigated in Lema\^{\i}tre - Tolman (L-T) and
quasispherical Szekeres (QSS) spacetimes. In the present paper, an axially
symmetric QSS deformation is superposed on such an L-T background that was
proved, in the first paper, to mimic several properties of gamma-ray bursts.
The present model makes $z$ closer to $-1$ than in the background L-T
spacetime, and, as implied by the second paper, strong blueshifts exist in it
only along two opposite directions. The QSS region is matched into a Friedmann
background. The Big Bang (BB) function $t_B(r)$, which is constant in the
Friedmann region, has a gate-shaped hump in the QSS region. Since a QSS island
generates stronger blueshifts than an L-T island, the BB hump can be made lower
- then it is further removed from the observer and implies a smaller observed
angular radius of the source. Consequently, more sources can be fitted into the
sky - all these facts are confirmed by numerical computations. Null geodesics
reaching present observers from different directions relative to the BB hump
are numerically calculated. Patterns of redshift across the image of the source
and along the rays are displayed.
