  Squeezed spin states have important applications in quantum metrology and
sensing. It has been shown by S{\o}rensen and M{\o}lmer [Phys. Rev. A 66,
022314(2002)] that an effective one-axis-twisting interaction can be realized
in a cavity setup via a double off-resonance stimulated Raman scattering,
resulting in a noise reduction scaling $\propto 1/N^{2/3}$ with $N$ being the
atom number. Here, we show that, by making an appropriate change of the initial
input spin state, it is possible to produce a one-axis-twisting spin squeezing
via a \emph{single} off-resonance stimulated Raman scattering, which thus can
greatly simplify the realistic implementation. We also show that the
one-axis-twisting interaction can be transformed into a more efficient
two-axis-twisting interaction by rotating the collective spin while coupling to
the cavity, yielding a Heisenberg limited noise reduction $\propto1/N$.
Considering the noise effects due to atomic decoherence and cavity decay, we
find that substantial squeezing is still attainable with current laboratory
techniques.
