  We present methodology to derive high-precision estimates of the fundamental
parameters of double-lined spectroscopic binaries. We apply the methods to the
case study of the double-lined beta Cephei star beta Centauri. We also present
a detailed analysis of beta Centauri's line-profile variations caused by its
oscillations. We point out that a systematic error in the orbital amplitudes,
and any quantities derived from them, occurs if the radial velocities of
blended component lines are computed without spectral disentangling. This
technique is an essential ingredient in the derivation of the physical
parameters if the goal is to obtain a precision of only a few percent. We have
devised iteration schemes to obtain the orbital elements for systems whose
lines are blended throughout the orbital cycle. We find the following
parameters for beta Cen: $M_1=10.7\pm 0.1 M_\odot$ and $M_2=10.3\pm 0.1
M_\odot$, an age of $(14.1\pm 0.6)\times 10^6$ years. We deduce two oscillation
frequencies for the broad-lined primary of beta Centauri with degrees higher
than 2. We propose that our iteration schemes be used in any future derivations
of the spectroscopic orbital parameters of double-lined binaries with blended
component lines to which disentangling can be successfully applied.
