NEW YORK (CNN/Money) - With the New York Stock Exchange reeling from recent scandals, calls are mounting for the world's largest stock exchange to revamp its trading system.

And investors are bidding up some lesser-known players in anticipation of possible big changes in the way stocks are traded on Wall Street.

Is the NYSE specialist system in need of reform? Richard Repetto, research analyst with Putnam Lovell NBF, talks about the specialist system. Play video (Real or Windows Media)

The NYSE uses traders known as specialists to match customer orders, and when there is an imbalance in orders, the specialists and their firms commit their own money to ensure orderly trading in the stocks.

Critics' allegations of improper trading, complaints about the specialist system, as well as more recent questions about the exchange's exorbitant pay packages and its governance policies have left some investors and listed companies grumbling.

The exchange gets about 560 complaints about stock trading each year from listed companies, investors and traders, an NYSE spokesman said Monday.

The latest wrinkle in the NYSE's troubles? One of the world's biggest pools of investment capital, mutual fund firm Fidelity Investments, recently approached NYSE officials, including interim Chairman John Reed, about replacing the specialist system with an electronic system, CNNfn confirmed Tuesday.

American International Group, the No. 1 U.S. insurance firm and a company listed on the NYSE, has also expressed its displeasure with the specialist system.

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"If the specialist cannot effectively perform his role, then we need to look for alternatives including the electronic matching of buyers and sellers, with no human intervention," AIG CEO Maurice Greenberg wrote last week in a letter on AIG's Web site.

Although the NYSE is clearly the biggest and highest-profile exchange, it's not the only game in town.

There's the archrival Nasdaq market, of course, as well as two large but lesser-known electronic communication networks (ECNs): closely held Archipelago and its bigger rival, publicly traded Instinet Group.

Stock of Instinet (INET: up $0.05 to $5.80, Research, Estimates) jumped about 16 percent Tuesday, after it already more than doubled over the last year, on news of Fidelity's push for an electronic trading market.

Meanwhile, the stocks of the NYSE's specialist trading firms sank after the comments by Fidelity, one of Wall Street's largest customers. LaBranche & Co. (LAB: Research, Estimates) shares tumbled 6.8 percent while the NYSE-listed shares of

Netherlands-based Van der Moolen (VDM: Research, Estimates) fell 4.1 percent.

Under rules meant to insure that investors get the best price for their stock trade, Archipelago and Instinet are allowed to execute trades in NYSE-listed stocks, but in practice they account for only up to 4 percent of NYSE volume, according to the Exchange.

The limits are due to the Intermarket Trading System, or ITS, part of the national market system developed in the late 1970s that allows electronic orders sent to the NYSE to be rejected by the exchange's specialists within 30 seconds, with a reason.

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The NYSE's specialists want to keep as many trades as possible for themselves since that's how they get paid.

"Of greatest concern are certain provisions of the Intermarket Trading System," Instinet said in a recent statement. "Those rules, adopted with traditional floor-based markets in mind, negate the speed and certainty of electronic markets, inhibiting efficient trading, stifling transparency, widening spreads and increasing transaction costs."

The NYSE spokesman was not immediately available for comment Tuesday.

An Archipelago spokeswoman said the SEC is looking at possibly reforming the ITS as part of a restructuring at the NYSE and is already doing a trial reform that was recently extended through next March.

It's very possible the ITS will be reformed, and that could open some doors for Instinet, according to Michael Vinciquerra, analyst with Raymond James & Associates, who has a "market perform" rating on the stock.

"What Instinet needs is a boat-load of volume," he said. "They essentially make 0.1 cent per share traded, so it's difficult for them to make money in the current conditions."

Wall Street sees that trend continuing for Instinet. Analysts expect the company will report a breakeven third quarter, which also makes the stock hard to value, Vinciquerra added.

However, he noted that the company will be meeting with analysts and investors within the next month, and this could shed some light on the health of its businesses.

"If more NYSE volume is moved away from the exchange, the ECNs are a logical place for it to go. If that happens, they could get it turned into a profitable company again," he said.  

--Vinciquerra does not own Instinet shares, nor does Raymond James have a banking relationship with the company. It does make a market in Instinet shares, however.