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One-stop shopping is a terrific concept, so long as you can actually get everything you want in one place.

Depending on your habits as a mutual fund investor, you might be able to find such a place among the online brokerage firms.

Online brokers have plenty to offer fund investors, from the convenience of consolidated statements and one-stop shopping in their fund supermarkets to research tools and recommended lists. But many also have hidden frustrations, notably fee structures and policies that range from restrictive to downright stupid.

“There is a lot to be said for having everything in the same place, where you can see all of your investments on one statement and manage everything together,” says Kurt Cerulli, of the Boston research firm Cerulli Associates, which studies trends in the fund marketplace. “The question people need to answer is whether the convenience is worth the cost, and what, if anything, you give up for the sake of that convenience.”

That being the case, anyone looking to consolidate accounts or simply to buy funds through an online brokerage should shop around, paying particular attention to the following:

– Available funds. The leading online brokerages offer anywhere from 2,000 to 10,000 funds, sufficient for almost everyone provided that the funds you want are in the mix.

Ameritrade, Datek and E*Trade, for example, all don’t carry Fidelity funds. And you won’t be able to consolidate all your accounts if you own funds that are outside the broker’s program.

It’s not always easy to check out which funds a firm offers. Some firms only show their fund list to existing customers, others show only the fund families they carry (which is misleading if they don’t handle all funds from within a family). If a firm won’t show you the available funds before you open an account, move on.

– Fees. The big worry here is “transaction fees,” which essentially is the brokerage’s commission on the trade and which can apply even when you are buying a fund that normally carries no sales charge. While a typical range would be $15 to $35, transaction fees can run as high as $75 or a percentage of the amount being invested. (The transaction fee is waived on funds that carry a sales charge, but you still have to pay the load on those funds.)

Most fund supermarkets offer some funds at no charge, so find out what’s available on a “no-transaction-fee” (NTF) basis. A supermarket may claim to offer 10,000 funds, but none of the biggies have more than 2,000 NTF funds.

Other fees to worry about include setup charges and transfer fees — calculate the cost of moving and consolidating everything so you can decide if the convenience is worth it — and short-term trading fees. Not all firms have short-term fees, but those that do will ding you for upwards of $30 if you sell a fund within six months or a year of purchase.

– Account minimums. This is a strange issue, one where the fund marketplaces can hurt or help depending on circumstances. Some brokerages set their own minimum purchase amounts, particularly on the NTF funds. That means a fund with a $2,500 minimum in the outside world may require twice that much through a brokerage.

There are times, usually on funds with minimums above $10,000, when the brokerages actually let you open an account for less money than the fund normally requires. The rules vary from one brokerage to the next, so check before you sign up.

– Trading rules. The short-term fees applied by the big brokerages should tell you that this is not a place to go trading funds. On top of that, however, is the fact that a few of these firms close out the trading day early. Ordinarily, if you sell a fund while the market is open (until 3 p.m. Chicago time), you get the day’s closing price; at some supermarkets, if you sell after 2 p.m., your trade doesn’t go through until the next day.

– Research capabilities. Some firms offer a list of funds that their analysts prefer, others provide virtually nothing. You can, of course, research funds on your own at sites like Morningstar.com, but since research is part of what you are paying for at a brokerage, it’s good to get your money’s worth.

– Dividend reinvestment/automatic investment programs. Not every brokerage firm lets you roll over dividends (they may sweep such money into the house’s money market fund), and some will not let you establish an automatic investment plan or will charge you a fee to do it.

“Because most fund families allow automatic investment but many brokerage firms don’t, this is something that people could be giving up when they go to a brokerage,” says Jamie Heller, editor at large of TheStreet.com, who recently examined the policies of the major online brokerages. “If you like to save money automatically, a lot of the firms aren’t right for you.”

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Chuck Jaffe is mutual funds columnist at The Boston Globe. He can be reached by e-mail at jaffe@globe.com or at The Boston Globe, Box 2378, Boston, Mass. 02107-2378.