According to five people briefed on the relationship who requested anonymity because they didn’t want to damage continuing business relationships, Goldman told Thornburg that the request was justified because the value of similar mortgages traded by other parties had been priced at lower levels. But Goldman, according to two people with knowledge of the situation, had not actually seen such trades.

Thornburg officials, however, pushed back on Goldman’s request, questioning the values the firm put on Thornburg’s portfolio. “When we tried to negotiate price, they argued that they were aware of transactions that were not broadly known on the Street,” said a former Thornburg employee briefed on the talks with Goldman. “That was their justification for why they were marking us down as aggressively as they were — that they were aware of things that others were not.”

Even as Goldman pressured Thornburg for cash, a Goldman banker pitched Thornburg to hire the firm to help it raise new funds. Thornburg turned elsewhere.

Thornburg wasn’t the only firm Goldman pressured this way. It made similar demands — using similar arguments — of A.I.G., the insurer that stood behind many of Goldman’s mortgage securities. Ultimately, Goldman’s demands drained the insurer of so much cash that a hobbled A.I.G. required a taxpayer bailout in September 2008. Meanwhile, Goldman had been buying protection against a possible debt default by A.I.G. at the same time that it was pressuring A.I.G. to pay it additional cash. Because Goldman’s own cash demands were weakening A.I.G., Goldman had a front-row seat to the distress the company was experiencing — giving Goldman added insight that buying default insurance on A.I.G. was probably a shrewd investment.

Although Goldman’s financial insight derived from proprietary dealings with A.I.G., and included facts that others in the market most likely didn’t have, Mr. van Praag, the Goldman spokesman, said that his firm was not capitalizing on nonpublic information.

Like A.I.G., Thornburg found that arguing with Goldman was fruitless, because the firm had favorable contracts with Thornburg governing disputes. So Thornburg accepted Goldman’s valuations, but then established credit lines with other banks.

Although Goldman lost a customer, its mortgage unit had gained a victory: the firm could cite the valuations that Thornburg accepted as proper pricing for mortgage securities when it got into similar disputes with other clients.