Several shareholders are seeking to tighten the screws on Tesla's CEO Elon Musk following last month's SEC charges.

Several Tesla Inc. (TSLA - Get Report) shareholders -- including CtW Investment Group -- have demanded that the auto company's board tighten the reins on CEO Elon Musk beyond measures already agreed to in an SEC settlement, according to a letter posted on CtW's website.

The shareholders wrote to the board seeking changes in governance following the recent settlement between Tesla and the Securities and Exchange Commission over Musk's tweeted claim he planned to take the company private.

The list of demands include:

* Permanently separating the chairman and CEO positions -- dual jobs long held by Musk. 

* Creating a "robust refreshment plan" for board members.

* Setting a timeline for directors to exit, including "off rotation" plans for "non‐independent directors" such as Antonio Gracias and Kimball Musk, who both have either personal or financial ties to Elon Musk, according to the letter.

* Diversifying the candidate pools for new directors.

Among the letters signatories are Denise L. Nappier, Connecticut state treasurer; Tobias Read, Oregon's state treasurer and Scott M. Stringer, New York City comptroller.

The letter follows a Sept. 29 agreement between Tesla and the SEC to settle a securities fraud charge from earlier in the month. The agreement was designed to lead to "comprehensive corporate governance and other reforms" at Tesla, according to the SEC. Those changes included removing Musk as chairman of the board for three years; imposition of $40 million in penalties from Tesla and Musk; selection of an independent chairman; and appointment of two new independent directors to the board. New controls were to have been put in place  to "oversee Musk's communications."