NEW YORK, May 10 (Reuters) - Crown Castle co-founder Ted Miller suffered a setback on Friday when a prominent proxy advisory firm urged investors to back the wireless tower owner's director nominees instead of the four people he wants shareholders to elect to the board.

Institutional Shareholder Services (ISS) wrote there is "no case for incremental change at this juncture" after prominent activist investor Elliott Investment Management pushed for changes late last year and the company took quick action.

Crown Castle, with a market value of $43 billion, now has a new chief executive officer, is reviewing the future of its fiber business and added new directors, including Elliott portfolio manager Jason Genrich.

Miller, who served as Crown Castle's CEO between 1996 and 2002, when he resigned, and now runs investment fund Boots Capital, also wants the company to sell the fiber business.

He argued that he and his partners should join the board so they could help find a buyer for the business and assist the company in upgrading its tower assets.

Boots Capital's slate includes Miller, his son-in-law Tripp Rice, Charles Green and David Wheeler. Shareholders will elect four directors on May 22 to serve on the board that now has 13 members.

Miller also pushed the company to let shareholders vote on what he called a "coercive and disenfranchising" agreement with Elliott.

ISS, whose recommendations guide many investors on how to decide hot-button issues including who serves on boards and whether companies should merge, said change was needed when Elliott arrived, first in 2020 and then again in 2023.

But the hedge fund's criticisms, which partly overlap with Boots' concerns, are being addressed, ISS wrote.

Boots' offer to assist with changes that are already being implemented, is not necessary, the ISS report said.

"In light of the improvements to the board composition and governance, the new CEO, and the strategic review initiated as a result of Elliott's campaigns in 2020 and 2023, incremental changes at the board level do not appear necessary," the report seen by Reuters said.

Representatives for Crown Castle did not have an immediate comment and a representative for Boots did not immediately respond to a request for comment.

(Reporting by Svea Herbst-Bayliss Editing by Bill Berkrot)