Brazilian law fully recognizes the concept of party autonomy (autonomia da vontade), subject only to matters of public policy (ordem pública) and morality (bons costumes). Therefore, parties to an arbitration agreement have freedom to either lay down the rules of procedure of their proceedings empower the arbitral tribunal to do so (as long as the selected rules of procedure comply with the following principles: (i) adversarial system; (ii) equal treatment of the parties — giving each party a reasonable opportunity to present its case—; (iii) impartiality; and (iv) arbitrator’s freedom of decision).
One Brazilian scholar understands that is possible for the parties to select a foreign law as the procedure law of arbitration, provided that such foreign law comply with the principles mentioned above, in the preceding paragraph [CARLOS A. CARMONA, ARBITRAGEM E PROCESSO 28 (1998)].
If the parties fail to select the arbitration's rules of procedure —or if they fail to indicate that this will be a resolution of the arbitral tribunal—, the arbitral tribunal is then authorized to take such decision, as it considers appropriate, as per Section 21(1) of the Brazilian Arbitration Act (“BAA”).
Brazilian law allows some "discovery": Section 22 of the BAA lays down that the arbitral tribunal —either at its own discretion or at the parties' request— may take the parties' deposition, hear witnesses, and determine the production of expert witness reports or other evidence. Parties may opt for the use of the IBA Rules on the Taking of Evidence in International Commercial Arbitration, a sort of “model discovery rules”, but US-style discovery is not permitted in international arbitrations where Brazilian law is the lex arbitri.
It is fair to say that BAA gives the parties —and the arbitrators— great freedom and flexibility to agree upon the arbitration rules.