In 1565, while Muñoz was still serving on the Council of the Indies, the Second Marqués del Valle de Oaxaca and Luis Cortés, both sons of Hernán Cortés, led a conspiracy to declare the independence of New Spain. The conspiracy was suppressed and some of the conspirators, including the sons of Cortés, were arrested. Before the arrival of the new viceroy, Gastón de Peralta, marqués de Falces, the Audiencia had had two conspirators executed, and had sentenced Martín and Luis to death. Upon his arrival, Peralta reviewed the cases and suspended the death sentences given the sons of Cortés. They were sent back to Spain to be dealt with by the Council of the Indies. The Audiencia denounced the new viceroy for his friendship with the rebels.