The bankers at Goldman Sachs (GS ), by traditional measures, ought to be on top of the world. Eighteen months removed from the depths of the financial crisis, Goldman posted a $13.4 billion profit in 2009, a Wall Street record. When Chief Executive Officer Lloyd Blankfein went on a recruiting trip to Stanford, he was greeted by an overflow crowd. Goldman cast off its Troubled Asset Relief Program yoke and proceeded to pay its employees more than $16 billion. The firm is moving into a new $2.1 billion headquarters on the Hudson River.

Goldman’s reputation with its clients—who must have at least $10 million to open an account—has never been better. Among the general public, however, the perception is that Goldman is the toxic epicenter of everything wrong with Wall Street. The firm’s 32,000 employees are seen as an army of Gordon Gekkos, greedy manipulators who pumped up the housing bubble, then bet opportunistically on its implosion as American International Group (AIG ), its trading partner, buckled under massive debts. It is widely alleged—though unproven—that Goldman called on its close friends in government to arrange for an AIG bailout, effectively pocketing billions of taxpayer dollars. Every game has a sucker, says William K. Black, a professor of law and economics at the University of Missouri at Kansas City who was deputy director of the Federal Savings & Loan Insurance Corp. and in this case, the sucker was not so much AIG as it was the U.S. government and taxpayer.

Heads Goldman wins, tails you lose, America.

All this public opprobrium has cut into the sublime contentedness that once came with making partner at Goldman Sachs. Executives warn that the firm’s position as the whipping boy for a public enraged by financial industry bailouts will crimp future profits. It now has few friends in Washington. Even the market is discounting Goldman, though the company commands the highest return on equity of any major bank—nearly four times JPMorgan Chase’s (JPM ). Today the market values Goldman Sachs shares at just less than half the book multiple at which they sold when Goldman went public 11 years ago. Changes have been made to compensation practices. The firm announced in December that its top 30 executives would, for one year, receive bonuses entirely in long-term stock. More than that, Goldman’s leaders say the vilification is unjustified. This, says Chief Financial Officer David A. Viniar, has been one of the most frustrating experiences of my 30 years with the firm.

The real story of what Goldman did is so much simpler than the conspiracy theories, says Viniar. Faced with a crisis they didn’t foresee, Goldman bankers merely did their jobs, no more and no less. The firm had no subprime agenda, no motives that were at odds with those of their clients. If they were half as smart and devious as the public believes, Goldman would have done far better than it did in 2008.

For the past year, as its name was sullied, Goldman maintained a bunker strategy, largely fending off media inquiries. (The one major exception proved to be a disaster. After Blankfein sat for an interview with the London Times in November 2009, he famously quipped, when he thought he was off the record, that he was just a banker doing God’s work.) That fleeting attempt at humor created a weeks-long media storm, after which Goldman stopped trying to defend itself.

Now, Goldman has shifted tactics. On Apr. 7 it will release its 2009 annual report with a letter to shareholders that will, for the first time, explicitly defend its conduct during the mortgage bubble and subsequent collapse. In advance of that, the firm made available to Bloomberg BusinessWeek several top officials, including Viniar; Harvey M. Schwartz, who is co-head of the global securities division, which includes the derivatives and mortgage trading desk; and Craig W. Broderick, the firm’s top risk manager.

Blankfein was not made available, despite repeated interview requests. Over the course of a week the interviews addressed three major allegations: one, that Goldman duped AIG and, subsequently, the U.S. government, into paying fully for credit-default swaps insuring mortgage securities; two, that it took short positions on the collateralized debt obligations that it had created and sold to clients (thereby betting against them); and three, that it stuffed these CDOs with inferior mortgage assets that ensured their collapse.

The defense mounted by Goldman lacks critical details, a consequence, the firm argues, of its overriding need to protect the confidentiality of its clients. But the overall message was emphatic and unified: Goldman did nothing for which it owes anybody an apology—and it doesn’t owe anybody any money, either. Its brilliance has been wildly overestimated. Goldman managers were smart, but not that smart. Above all, Goldman insists it played by the same rules as everyone else.

By way of background: Twelve years ago, right out of college, I worked at Goldman Sachs for two years. The training program was all about culture. Keep your head down. Never get your name in the newspaper. Wear conservative blue or white Oxford shirts and don’t ever be ostentatious in public. Goldman, the partners told us, swore by the corporate philosophy of long-term greedy, as set out by the revered Gustave Levy, senior partner at the firm in the early 1970s. The stated ethos was to turn down easy money and build relationships. So walk on eggshells, kid—and fix your tie.

Within months of my start date in 1998, Goldman was going through a vigorous internal debate over whether to go public. Some warned that this would open up the storied partnership to untenable scrutiny from the outside world. With brokerage commissions disappearing and hedge funds coming into their own, did Goldman Sachs need to ratchet up its risk profile so it could continue to be a major player on Wall Street? Or should it consolidate its gains and be more of a humdrum asset manager?

Goldman did go public in May 1999, and while management assured shareholders the firm would continue to derive the bulk of its revenue from investment banking and asset management, Goldman did increase its risk profile and, under Blankfein’s leadership, rapidly reorient itself from banking to trading. Profits soared, and the firm built a new headquarters. Situated just northwest of Ground Zero, it is heavily guarded—men in blazers with walkie-talkies abound—and you would be hard-pressed to find the words Goldman Sachs anywhere within, save for maybe the pencils in the supply cabinet. The place is foreboding and hush-hush quiet.

After taking three pre-programmed elevators, accompanied by a series of well-groomed handlers, I was escorted to a conference room with giant windows and views of AIG’s famous tower on Pine Street (which it sold last year).

I was greeted by Schwartz, 46, whose division brought in about 78% of the firm’s overall revenue last year. That includes the trading of stocks, bonds, currencies, commodities, and derivatives like CDOs—those pools of subprime mortgages on which AIG provided credit protection and which proved to be the insurer’s undoing. Schwartz, more suburban tee-ball coach than Hermès-clad master of the universe, had just broken his shoulder while skiing. His arm was in a sling.

The conversation was genial and moved briskly to the most serious and widely repeated charge against Goldman: that it preyed on the poor judgment of AIG by buying more credit-default swaps from the company than it could ever conceivably pay out and then drove the company into insolvency by demanding that it post collateral for its deteriorating positions.

Defending Goldman, Schwartz grew agitated. The notion that Goldman Sachs took down AIG is one of the greatest fallacies of the entire crisis, he insists, one open palm flailing in the air. It’s categorically impossible for us to take down a firm.

The AIG-related charges against Goldman go further. Critics such as AIG’s former chief executive, Maurice R. Hank Greenberg, have contended that Goldman caused AIG’s demise and that Goldman should have known, as basic due diligence, that AIG was in way over its head.

Hogwash, says Goldman. Although in hindsight it appears obvious that AIG was a patsy, that was not known when those deals were made. At that time, AIG was widely regarded as the world’s foremost insurance company, with a triple-A credit rating. It sold all manner of insurance on U.S. mortgage bonds to investment banks, including Merrill Lynch (now subsumed by Bank of America (BAC )), France’s Société Générale, and Germany’s Deutsche Bank (DB ). Goldman insists that it didn’t know AIG was in trouble until the third quarter of 2007 when it was too late. AIG was premier, most creditworthy, and most sophisticated—they looked like the perfect counterparty, says Broderick, Goldman’s chief risk officer, whom I spoke to on the phone. I had honestly no conception until late in the process that AIG was in as bad straits as they were.

Some of the deals with AIG, says Goldman, were plain vanilla. In those, Goldman created CDOs by acquiring pools of mortgage-backed bonds. Goldman says it then hedged these positions by purchasing insurance from AIG’s Financial Products unit in the form of credit default swaps. In other cases the deals were more exotic, with hedge funds looking to short the mortgage market coming to Goldman for help in structuring a derivative trade known as a synthetic CDO. From 2005 to 2007, Goldman issued $32.6 billion worth of both types of CDOs. As part of its insurance contract, AIG agreed to pay collateral to Goldman if the market value of a CDO dipped by more than 4%. Goldman checked the market prices daily and made numerous collateral calls on AIG beginning in mid-2007. By September 2008, Goldman had $7.5 billion of AIG’s money and claimed it was owed an additional $2.5 billion.

The incessant collateral calls caused the relationship between the two financial giants to deteriorate, with AIG claiming Goldman marked its CDOs lower than other banks’ and that it refused to accept the assessment of neutral third parties. (AIG declined to comment.)

Goldman’s counter-argument is that its CDO marks were properly conservative, and that it did what other banks would later be criticized for neglecting to do. Competitors dragged their feet in marking down their CDOs because it would have required them to take losses on their entire mortgage inventories.

In the end, Goldman asserts, the secret to its success was not that it was smarter than AIG or could divine the future any more clearly or that it had all those government connections that enabled it to get paid in full. Rather, Goldman’s advantage, it says, was that it did the dull, unglamorous work of repricing its securities at true market value, a Goldman hallmark since its days as a tight-knit partnership, when screwups came right out of partners’ capital. Although that’s not the case anymore, Viniar, the CFO, says the approach he takes is the same. I personally see the profit-and-loss statement of each of our 44 business units every single night, says Viniar. At a now-legendary meeting on Dec. 14, 2006, he says, Goldman executives, jittery after 10 straight days of losses in their mortgage portfolio, literally went through almost every position we had on the mortgage desk.

That’s when the decision was made to pare back Goldman’s exposure to the housing market. Contrary to popular belief, the firm did not make an about-face and short the market. Rather, the decision was to take a neutral position. I wish we knew as much as people are giving us credit for knowing, says Viniar. Nobody—certainly not us—knew the depths of the financial crisis we were going to face.

Beyond duping AIG, Goldman has been accused by Greenberg and others of selling mortgage securities to pension funds and other investor clients, then shorting the market. In other words, it has bet against its own clients.

Schwartz, exhaling loudly, says the very notion reveals a fundamental misunderstanding of Goldman’s reason to exist: market-making, or connecting buyers with sellers. In the ebb and flow of the market, buyers and sellers can’t always be immediately matched, so market makers often have to step in with their own capital to execute a trade for a client who demands one. Market-making has its attendant risks, but these are cushioned by fees on the trade flows in both directions. Although market-makers don’t necessarily make a directional bet on the market, they do often lean one way or the other. But, Goldman insists, it never took a big, one-way directional bet against the mortgage market. When it went short, Goldman says it did so chiefly to allow clients to bet that mortgage securities would plummet. It facilitated such deals by first buying mortgages with its own money. To protect its hide, Goldman then went out in the market to buy credit default swaps, putting it in a position to demand collateral if its own long position went south.

Although Goldman refuses to identify specific clients, multiple sources familiar with its business confirm that investors helped by Goldman in shorting the mortgage market included now-famous hedge fund manager John Paulson, whose fund made $20 billion over two years by betting that subprime mortgage prices would crater. Dr. Michael Burry, another mortgage-market seer and a prominent character in the Michael Lewis book The Big Short. was also a Goldman client, according to these same sources.

Viniar won’t say that Goldman never took a short position on securities it sold to clients—I could never use the word never, he says. Viniar’s point is that it wasn’t standard practice, that Goldman didn’t tell clients to do one thing while it did the opposite.

In part, says Viniar, that was because there was hardly consensus within Goldman about the state of the housing market. The decision after that 2006 meeting was to pare its mortgage exposure and come closer to home, meaning a more neutral stake. We were less long in 2007 to 2008, and that clearly saved us billions in potential losses, points out spokesman Samuel Robinson. We still lost money, but less than we would have otherwise.

Having adopted a neutral policy on mortgages, says Schwartz, Goldman continued to sell mortgage securities to clients who believed prices would keep climbing. Goldman would never have imposed its bias on clients. You can’t be so arrogant as to accept one view over another, or to abandon your market-making role when clients expect you to make markets every day, says Schwartz.

If the firm had acted more like some James Bond villain conspiring to plunder Main Street—as has been alleged by the ideologically diverse likes of Glenn Beck, Michael Moore, and Rolling Stone’s Matt Taibbi—it could surely have made a ton of money shorting the doomed mortgage market, say Goldman executives. The firm’s mortgage-related revenue from 2003 to 2007, says Schwartz, was less than 2% of total revenue—chump change. That includes underwriting and trading of residential mortgage bonds and CDOs, both for clients and Goldman’s own account. In 2008, Goldman actually lost $3.1 billion on its mortgage-related positions.

Goldman also says that, with one minor exception, it never sold CDOs at a retail level, to pension funds or municipalities, and instead dealt only with hedge funds, insurance companies, and large financial institutions, so-called qualified buyers that, under SEC rules, are expected to understand the risks.

In its letter, Goldman will stress that its CDO customers had access to expert advice and research. The only pension fund that bought its CDOs was a large, corporate-related fund long active in this area, and it only bought $5 million worth. (Goldman declined to name the company.) These investors, Goldman executives say over and over again, in telling unanimity, were sophisticated. Blankfein himself used the word several times in his contentious Financial Crisis Inquiry Commission testimony on Jan. 13.

The adjective is tactically (and somewhat tactfully) employed to argue that these clients were fully consenting adults and that Goldman cannot be held responsible for facilitating their bad decisions.

The third major allegation against Goldman gets right into the dirty details of what went into the CDOs, or what became known as toxic mortgages. Critics such as Janet Tavakoli, president of Chicago advisory firm Tavakoli Structured Finance and a onetime Goldman mortgage analyst, accuse the firm of cynically loading them up with bad loans so that when they blew up the firm could profit from the insurance it took out from AIG. Tavakoli notes some of the mortgage pools underlying Goldman-arranged CDOs were downgraded within six months of the issue—a telltale sign, she says, that Goldman was gaming a weakening system.

To Tavakoli, Goldman was, in some cases, able to take advantage of a flaw in the CDO system: AIG wrote credit protection on the basis of a mythical triple-A rating, while Goldman’s calls on AIG’s cash were based on its reality-tested valuations of the underlying mortgages. In other words, Goldman could quickly squeeze AIG for cash by marking down the mortgages underlying a CDO insured by a credit-default swap from AIG. Goldman created a no-lose situation for its clients, at AIG’s expense.

Now, says Tavakoli, indignantly, Goldman is trying to pretend it didn’t know any better, while also trying to say they are great risk managers. Goldman cannot have it both ways.

Here again, Goldman officials claim they were simply servicing the needs of clients. There was a lot of back and forth with the client, whether a hedge fund or someone else, to shape the needs of that client, according to a Goldman official who requested anonymity because he doesn’t want his name in the press. We were facilitating a client inquiry. But clients never dictate terms. Because of Goldman’s refusal to reveal the names of clients it was actually working on behalf of, this position is impossible to confirm. Such is the opacity of modern Wall Street firms; you can never quite tell when the firm is trading on behalf of its clients or on its own account. This opacity works very much to the advantage of the firms.

On one point regarding its CDO performance, however, Goldman has third-party backing. A study of about 700 CDOs underwritten between 2002 and 2007 concluded that Goldman’s CDOs performed better than all other major underwriters’. JPMorgan Chase’s rate of default was four times higher. That academic study did not come with elite bona fides; the author was a senior at Harvard University who has since been hired by Goldman.

For all of Goldman’s critics, some believe the firm deserves credit for keeping its eye on the ball, especially at a time when money was pouring in and competitors were getting lazy. The frikkin’ CFO of Goldman Sachs actually hauled the mortgage traders into his office and talked to them, says Kenneth Posner, the former head of Morgan Stanley’s financial services research group and author of the book Stalking the Black Swan. Other banks just did not roll up their sleeves that way.

But even Posner asserts that Goldman would have been a goner if the Fed didn’t throw it a life preserver by paying off AIG’s credit default swaps at 100 cents on the dollar and giving Goldman bank-holding-company status, which allowed it to borrow from the Federal Reserve at near-zero interest rates. Moreover, Goldman’s $10 billion in TARP funds, since paid back with interest, helped it maintain the aura of solvency at a time when the mere perception of weakness could have caused a run on the bank.

Goldman vigorously disputes that it could not have survived if the government hadn’t paid it in full. Of the $12.9 billion it received, Goldman produces math showing that only a relatively small amount—$2.5 billion—was actually a new transfer of funds to the firm itself. Goldman used some of the rest to close out a loan to AIG for which Goldman had full collateral.

The remainder Goldman paid to its own counterparties to acquire the mortgage securities underlying the credit default swaps AIG had written, which Goldman handed over to the Fed. So while the firm certainly would not have wanted to receive less than a full payout, its survival did not depend on it. This, it contends, quashes the notion of a back-door bailout that saved Goldman from extinction.

Talking to top Goldman executives, I couldn’t resist asking the obvious question: If the firm could just write a multibillion-dollar check to erase the outrage—deserved or not—over the AIG payout and be done with the public agony, wouldn’t it just do it? The question elicited sighs of exasperation and created some tension; I just wasn’t getting it. No, was the answer. The executives all agreed that would be an implicit admission of guilt, and Goldman Sachs isn’t guilty of anything.

In a Feb. 26 filing with the SEC, Goldman acknowledged that adverse publicity can have a negative impact on our reputation and on the morale and performance of our employees, which could adversely affect our businesses and results of operations. Officials say that several times the Justice Dept. has requested information soon after negative stories have appeared in the press. Eyebrows were certainly raised when the Treasury Dept. in late March chose Morgan Stanley over Goldman Sachs to handle the lucrative business of selling off the government’s $32 billion stake in Citigroup. Might Goldman’s tarnished reputation have caused it to lose out? Goldman won’t say whether it bid on the job, though a government official confirms that it did.

Speaking about prospects more generally, Viniar says Goldman’s decision to explain its motives and actions during the crisis isn’t fleeting, that it is committed to changing its popular image. We believe our franchise is as strong as it has ever been and that our clients, our people, and our shareholders are happy with our performance, he says. But we’re also very aware of public opinion and the backlash against Wall Street, and we’re doing our best to address it.

When Goldman Sachs went public in 1999, the firm issued a statement about its business objectives. While we plan to continue to grow our trading businesses, the financial-market shocks of the past year underscored the importance of our strategy of emphasizing growth in our investment banking, asset management and securities services businesses, the statement read. Through a greater relative emphasis on these businesses, our goal is to gradually increase the stability of our earnings. The statement was an attempt to assure future shareholders that the Goldman culture would endure, that an investment in the firm that brought Ford Motor (F ) public and was crucial to so many American business success stories, would be a rock-solid investment. Goldman would be different from firms like Salomon Brothers that lived off the quick-hit profits of the trading desk.

A decade later, the percentage of revenue derived from trading and principal investment has ballooned from 55% to 76% in 2009. Business is booming, but Goldman, which once prided itself on avoiding the ostentatious and on making money for the long haul, is a different firm, with a perception problem that mere explanation can’t solve. In committing to market-making at all costs, the firm has opened itself up to forces beyond its control. The question is: Has Goldman Sachs shorted itself?