Chief Alonzo (or Alonza; newspaper accounts vary) E. Glenn had been a school attendance and probation officer prior to being appointed to succeed Chief Barbour after his resignation.  Prior to that office, he had been in the painting business.
Like his predecessors, Chief Glenn spent a lot of time dealing with traffic in downtown Raleigh.  Speeding continued to be an item of concern.  In May of 1920, he launched an anti-speeding campaign.  In the following August, the police began to crack down on cars without the property city license, those who failed to use both headlights while in the city, and drivers under the legal driving age of 16.
By February of 1923, Chief Glenn began to call for more personnel and equipment to help the police in their work.  Although they had made 230 arrest the previous month, the police could be much more effective if they could add a patrol of eight men, three more plainclothes detectives, and perhaps replace the one police vehicle at their disposal.  The most common causes of arrests continued to be either alcohol-related or speeding.
Chief Glenn was asked to resign by the city board of commissioners in August of 1924; at the time, they gave no reason for the request, leading some to speculate that it was a political move, or that he was being made a scapegoat for an embarrassing vice raid made some weeks earlier.  Alonzo Glenn worked as interior decorator after he left the police, eventually moving to Greensboro to stay with one of his daughters.  He died at her house after an illness of about four months, on August 8, 1941.  He was buried in Oakwood Cemetery.