  Given the failure of existing models for redshift-space distortions to
provide a highly accurate measure of the beta-parameter, and the ability of
forthcoming surveys to obtain data with very low random errors, it becomes
necessary to develop better models for these distortions. Here we review the
failures of the commonly-used velocity dispersion models and present an
empirical method for extracting beta from the quadrupole statistic that has
little systematic offset over a wide range of beta and cosmologies. This
empirical model is then applied to an ensemble of mock 2dF southern strip
surveys, to illustrate the technique and see how accurately we can recover the
true value of beta. We compare this treatment with the error we expect to find
due only to the finite volume of the survey. We find that non-linear effects
reduce the range of scales over which beta can be fitted, and introduce
covariances between nearby modes in addition to those introduced by the
convolution with the survey window function. The result is that we are only
able to constrain beta to a 1-sigma accuracy of 25% (beta=0.55 +/- 0.14 for the
cosmological model considered). We explore one possible means of reducing this
error, that of cluster collapse, and show that accurate application of this
method can greatly reduce the effect of non-linearities, improving the
determination of beta. We conclude by demonstrating that, when the
contaminating effects of clusters are dealt with, this simple analysis of the
full 2dF survey yields beta=0.55 +/- 0.04. For this model this represents a
determination of beta to an accuracy of 8% and hence an important constraint on
the cosmological density parameter Omega_0.
