The commission on Tuesday recommended three additional nominees - Deming lawyers Robert Floyd and Jarod Hofacket and Silver City attorney Timothy Garner.
The governor will consider the four candidates in filling a vacancy created by the retirement of District Judge Gary Jeffreys
in the 6th Judicial District of Grant, Hidalgo and Luna counties.
Martinez wanted more than one nominee to preserve her authority to fill the vacancy rather than having a nominating commission effectively make the selection by recommending a single candidate.