The Brillouin instability (BI) caused by stimulated Brillouin scattering (SBS) can limit the output power of high-energy laser amplifiers. Pseudo-random bitstream (PRBS) phase modulation is an effective modulation technique to suppress BI. In this paper, we study the impact of the PRBS order and modulation frequency on the BI threshold for different Brillouin linewidths. PRBS phase modulation with a higher order will break the power into a larger number of frequency tones with a lower maximum power in each tone, leading to a higher BI threshold and a smaller tone spacing. However, the BI threshold may saturate when the tone spacing in the power spectra approaches the Brillouin linewidth. For a given Brillouin linewidth, our results allow us to determine the order of PRBS beyond which there is no further improvement in the threshold. When a specific threshold power is desired, the minimum PRBS order required decreases as the Brillouin linewidth increases. When the PRBS order is too large, the BI threshold deteriorates, and this deterioration occurs at smaller PRBS orders as the Brillouin linewidth increases. We investigate the dependence of the optimal PRBS order on the averaging time and fiber length, and we did not find a significant dependence. We also derive a simple equation that relates the BI threshold for different PRBS orders. Hence, the increase in BI threshold using an arbitrary order PRBS phase modulation may be predicted using the BI threshold from a lower PRBS order, which is computationally less time-consuming to compute.