The Securities and Exchange Commission is cracking down on so-called greenwashing, but its latest proposals may still leave companies with enough room to define their own ESG standards.

There is an effort to stop the ESG label from being used too liberally. They came a week after Exxon Mobil was included in the S&P 500 ESG Index despite its focus on making oil and gas.

The SEC wants to raise disclosure requirements and target funds with naming practices. One proposal would expand the SEC's Names Rule to include ESG, meaning that a fund billing itself as focused on environmental, social or governance must invest at least 80% of its assets that way.

Another proposal would require ESG impact funds to give information about the greenhouse-gas emissions produced by the companies they hold, as well as how they measure progress on their goals. That may sound good for Exxon, but not so good forTesla.

While the SEC wants to tighten rules, it is also asking companies and funds to define their own ESG for themselves.

She told Insider that the commission has taken a free-market approach.

The EV maker was kicked out of the S&P 500 because it was low on the S&P's own ESG score.

The new proposals from the SEC may allow a green-energy company likeTesla to remain outside of the ESG index. Each company is weighted against one another in the same field. The issues with social and governance complaints still weigh on the company, even though it shines on environmental standards.

The proposal still gives private sector actors a lot of ability to define what it is, and it is likely to manifest through interactions between fund managers and their investors.