  We carefully reconsider the problem of classifying broad absorption line
quasars (BALQSOs) and derive a new, unbiased estimate of the intrinsic BALQSO
fraction from the SDSS DR3 QSO catalogue. We first show that the distribution
of objects selected by the so-called ``absorption index'' (AI) is clearly
bimodal in log(AI), with only one mode corresponding to definite BALQSOs. The
surprisingly high BALQSO fractions that have recently been inferred from
AI-based samples are therefore likely to be overestimated. We then present two
new approaches to the classification problem that are designed to be more
robust than the AI, but also more complete than the traditional ``balnicity
index'' (BI). Both approaches yield observed BALQSO fractions around 13.5 per
cent, while a conservative third approach suggests an upper limit of 18.3 per
cent. Finally, we discuss the selection biases that affect our observed BALQSO
fraction. After correcting for these biases, we arrive at our final estimate of
the intrinsic BALQSO fraction. This is f_BALQSO = 0.17 +/- 0.01 (stat) +/- 0.03
(sys), with an upper limit of f_BALQSO = 0.23. We conclude by pointing out that
the bimodality of the log(AI) distribution may be evidence that the BAL-forming
region has clearly delineated physical boundaries.
