  A small number of quasars exhibit interstellar scintillation on time-scales
less than an hour; their scintillation patterns are all known to be
anisotropic. Here we consider a totally anisotropic model in which the
scintillation pattern is effectively one-dimensional. For the persistent rapid
scintillators J1819+3845 and PKS1257-326 we show that this model offers a good
description of the two-station time-delay measurements and the annual cycle in
the scintillation time-scale. Generalising the model to finite anisotropy
yields a better match to the data but the improvement is not significant and
the two additional parameters which are required to describe this model are not
justified by the existing data. The extreme anisotropy we infer for the
scintillation patterns must be attributed to the scattering medium rather than
a highly elongated source. For J1819+3845 the totally anisotropic model
predicts that the particular radio flux variations seen between mid July and
late August should repeat between late August and mid November, and then again
between mid November and late December as the Earth twice changes its direction
of motion across the scintillation pattern. If this effect can be observed then
the minor-axis velocity component of the screen and the orientation of that
axis can both be precisely determined. In reality the axis ratio is finite,
albeit large, and spatial decorrelation of the flux pattern along the major
axis may be observable via differences in the pairwise fluxes within this
overlap region; in this case we can also constrain both the major-axis velocity
component of the screen and the magnitude of the anisotropy.
