Houghton served until 1850, when the New Mexico Territory was organized by one of the five acts of United States Congress collectively known as the Compromise of 1850.

The justices were given the same power to grant writs of habeas corpus as judges of the United States in the District of Columbia.

In 1951, Governor Ed Mechem voluntarily adopted a merit selection system, by the use of a judicial nominating committee that would recommend candidates for appointment.

From 1911 until 1988, New Mexico had been one of a decreasing number of states using an all-partisan election system to select Supreme Court justices.

In 1997, two District Court judges who lost their 1996 retention elections, along with individuals who had voted to retain them, challenged the constitutionality of the 57% requirement as invalid under the Equal Protection Clause of the Fourteenth Amendment to the United States Constitution, because it diluted the votes of those who favored the retention of incumbent judges.

The New Mexico Supreme Court granted certiorari and conducted oral arguments, but after a forty-minute deliberation ruled from the bench to dismiss the writ of mandamus.

The winning candidate serves out the remainder of the original term, at which time they are subject to a nonpartisan retention election requiring a 57% affirmative vote to remain on the court.

If the justice is not retained, they must vacate office on the following January 1, and the governor must again fill the vacancy by the ordinary procedures of appointment.

Whenever the governor fails to make an appointment within the prescribed thirty-day period, the Chief Justice fills the vacancy from the judicial nominating commission’s list of candidates.

[11] Additionally, whenever the governor fails to make an appointment to any court within the prescribed thirty-day period, the Chief Justice fills the vacancy from the judicial nominating commission’s list of candidates.