Because the positions are appointed by a judge they need independence because they rule on certain complaints against the city.
On Wednesday Mayor Berry said he wants the Hearing Office to report to the City Clerkâ€™s Office, also an independent agency.
â€śWe think by being in the Clerk's Office we will have a much better combination of some oversight but still a great deal of independence and we think that's the best of both worlds for the taxpayers of Albuquerque,â€ť Mayor Berry said.
City Councilor Dan Lewis is sponsoring the mayorâ€™s legislation which will go before the full council next week.
If approved it would go into effect immediately.
This would mean hearing officers would also be banned from having other jobs unless they clear it with the Mayor first.
Both Albertorio and Reina quit their city jobs after the investigation.
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New Mexico is located in the southwestern region of the U.S. Inhabited by Native American populations for many centuries, New Mexico has also been part of Imperial Spain, part of Mexico, and a U.S. territory.