Read MoreSEC chief wants to see changes in trading
Reforms White discussed are aimed at increasing transparency, eliminating unfair advantages for high-speed traders and possibly cutting back on the myriad of order types that algorithms employ to gain an edge over competitors. Some of those order types are never executed and can end up destabilizing markets.
White also expressed a desire to throw open the curtain surrounding "dark pools"—those trading platforms that occur away from the major exchanges and aren't required to make public their pricing activities.
However, the SEC chief also disagreed with a fundamental premise Lewis has espoused since the release earlier this year of his book "Flash Boys"—that markets are somehow "rigged" because of high-speed trading.
"Empirical evidence shows that investors are doing better in today's algorithmic marketplace than they did in the old manual markets. For institutional investors, the costs of executing large orders, measured in terms of price, were more than 10 percent lower in 2013 than in 2006," White said.
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"All of these market quality metrics show that the current market structure is not fundamentally broken, let alone rigged. To the contrary, the equity markets are strong and generally continue to serve well the interests of both retail and institutional investors," she added.
Many traders appreciated the vote of confidence in broad market structure, while agreeing with the notion that reforms are needed. For instance, Regulation National Market System, or Reg NMS, which mandates orders flow to the lowest price offered rather than fastest or most reliable platform, has attracted significant negative attention.
"Review of Reg NMS and allowing cross markets—many in the industry have said they think that's reasonable," Ross said. "That also would mitigate a big majority of the new order types that people are confused by. Those two kind of go hand in hand."
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As far as actual impact, though, most of the major trading outfits like the New York Stock Exchange, the Nasdaq and IntercontinentalExchange could see some impact though the latter two have indicated that HFT is not a big part of their respective businesses, according to an analysis Friday from Keefe, Bruyette & Woods:
We think stocks like KCG could see more headline risk around the various studies and proposals that could follow this because all of these hot-button issues relate to some of its business, and while it could benefit longer term from potentially wider spreads and reduced competition, in the meantime, there may be changes ahead. In addition, we continue to believe that activity that limits HFT activity or enforces more requirements around these firms to operate as market makers or dealers could be good for (Interactive Brokers).
KBW said it thinks one of the other changes that could emerge is wider price spreads, or ticks, for small-cap companies, which White noted have been put at a disadvantage in the HFT environment.
We estimate from the remarks that some near-term actions could involve changes around the faster trading, low execution volume dark pools could see more restrictions coming, which could bring volume back onto exchanges, limiting internalization. In addition we think the SEC is closer to a wider tick size pilot for small-cap companies in order to promote liquidity as part of a previous JOBS act pilot proposed. This could be good for market makers.
White said she expects the SEC to come up with recommendations for new rules over the next several months.
—By CNBC's Jeff Cox.