When most people think about identity theft, they often still think in terms of physical theft. There’s a classic image of a cat burglar rifling through your trash in the dead of night, pulling out bank statements and credit card offers and using them to steal funds or open fraudulent accounts in your name. It’s for this reason that identity theft experts recommend getting a shredder to destroy any sensitive documents before disposing of them.

Jim Van Dyke from Javelin Strategies, a financial services research firm, conducts an annual survey of identity theft victims. Stealing documents is just one way that thieves can get at your financial data. For this reason, Van Dyke says relying on shredding as your main line of defense represents an outdated approach. More important is implementing computer security safeguards, which include installing security software, using a password on your wireless router, and avoiding conducting financial transactions on public Wi-Fi networks.

Mobile security is also important, as people increasingly use Smartphone’s to conduct financial transactions and store data. It is important to use password protection on your phone and have a program in place that enables you to wipe the phone of sensitive data in the event that it’s lost or stolen.

It is also recommended that you download updated operating system software to make sure you’re up-to-date with the latest security patches. You should also consider a mobile security program, especially if you’re using a malware-prone platform like Android.

Even if you’re shredding every piece of paper in your home and taking every possible online security precaution, there are still methods of stealing your identity that are almost completely out of your control. Van Dyke says that his credit card number has been stolen on multiple occasions during transactions at local retailers, and he points out that a thief who doesn’t feel like rifling through your garbage can just as easily intercept incoming bank statements by opening your mailbox. For this reason, he says that your best tool is vigilance.

“Sign up for e-alerts (from your bank), monitor your statements electronically and turn paper documents off,” he advises. You might not be able to prevent every avenue of identity theft, but you can minimize the damage if you monitor your accounts and immediately notify the bank of unusual account activity.

The bottom line is that shredding protects you against only one form of identity theft, so account monitoring and online security should probably be your priorities. But even if identity thieves aren’t Dumpster diving as much as they used to, it would still be foolish to disregard the importance of document shredding.

“I think a lot of people assume that since so much is electronic, no one would go Dumpster diving,” says Shirley Inscoe, senior analyst for the Aite Group, a financial services research firm. “You would think that it’s a thing of the past, but in reality it’s really not.”

She points to the numerous documents that can be used to commit some form of fraud, a list that includes everything from bank statements to preapproved credit card offers to letters from your doctor or insurance company. Even an expired credit card can be used by a smart thief, so that too must be shredded before disposal.

“If you’ve got a fraudster familiar with the issuing financial institution, they can figure out what the new expiration date is,” she says. “It’s the same account number and the name is the same, so that info can be used to commit fraud.

And while it’s true that a shredder can’t protect you against a thief who simply steals those documents from your mailbox, Michael Barnett of the Identity Theft Protection Association says there’s a very good reason thieves may prefer Dumpster diving to mail theft.

“Stealing mail out of your box is a federal offense, whereas many courts have upheld that once you’ve thrown out your garbage, you no longer have an expectation of privacy,” he says.

So even in this digital age, a shredder is a must-have tool if you want to protect yourself from fraud. And it’s also important to remember that not all shredders are created equal, with some low-end models leaving pieces big enough for particularly ambitious thieves to reassemble. Earlier this year, for instance, a couple in Southern California were charged with committing check fraud by stealing and reassembling shredded documents from a self-storage facility, acquiring routing and bank numbers in the process.

It’s for this reason that some shredder manufacturers advertise that their product produces much tinier pieces than the competition, with “cross-cutting” models that turn your documents into confetti rather than spaghetti.

Such cases are, admittedly, rare. Van Dyke says it typically happens only in cases of corporate espionage, and Inscoe says she doesn’t have any personal experience with identity thieves going to such lengths. Nevertheless, Barnett says it’s worth paying a little extra for a top-of-the-line model that won’t leave anything that can be salvaged.

“Most thieves aren’t looking to reconstruct a jigsaw puzzle,” he says. “But the cost of a cross-cut shredder isn’t much more, and the extra security is worth the extra cost.”