"I think it's a practice that opens up a lot of questions with regard to markets and orders," said Joseph Mecane, executive vice president of NYSE Euronext, the company that runs the New York Stock Exchange.
The issue may be reaching critical mass; Schumer said on Tuesday that the head of the Nasdaq had assured him he supported a ban on flash trading.
Goldman Sachs called for curbs as well: "Anyone who has access to non-displayed information should assume the obligations of a market maker," said Canaday, using the term for a firm powerful enough to help set the prices for a stock. "Stronger standards are needed to make sure there is not a misuse of information."
It remains to be seen whether stronger standards will be imposed. A debate has broken out over the fairness of such super-fast stock trading.
"It does put more money in the marketplace," said Rick Bookstaber, a veteran risk manager at firms such as Morgan Stanley and Salomon Brothers. "What needs to be answered is whether it's money that does anything of social or economic value."