A growing number of lenders are courting borrowers who have been shut out of the mortgage market despite their sound financial circumstances. In particular, these companies see a burgeoning market in the self-employed as well as in households with a single negative credit incident, both populations that often struggle to obtain credit.

A recent analysis by the real estate website Zillow found that self-employed borrowers receive 40 percent fewer purchase loan quotes than other borrowers, mainly because of their typically lower credit scores. And many major banks remain reluctant to lend outside the guidelines for what are called qualified mortgages, or QM loans, which are salable to government-controlled agencies like Fannie Mae and Freddie Mac.

But investors are getting behind smaller lenders who are going beyond the qualified mortgage restrictions to analyze individual borrowers’ situations. To hedge the slightly higher risk, the lenders usually charge higher interest rates and require a down payment of at least 20 percent.

“If QM was a black-and-white view of credit, non-QM is more of the color version,” said Robert Hirt, the founder and chief executive of RPM Mortgage, a private lender based in Alamo, Calif.

RPM recently began offering a new loan program for borrowers who have substantial assets but are unable to obtain a mortgage because of an irregular income stream, a short or slightly scarred credit history, or a debt-to-income ratio above the 43 percent cutoff for qualified mortgages. The program is available in 12 states, Mr. Hirt said, and RPM is pursuing licensing in many more. The loans are available as 5/1 or 7/1 adjustable rate mortgages (with fixed interest rates for five or seven years) up to a maximum of $4 million. RPM sells the loans to a large asset manager.

As an example of its target borrower, Mr. Hirt described a recent client who, despite having “millions” in the bank and an 800 FICO score, could not obtain a qualified loan because of a short sale on a home in Florida three years ago. RPM approved a $1 million mortgage for a home on which the borrower made a 60 percent down payment.

“This isn’t about your subprime borrower — we are focused on extremely solid bets,” Mr. Hirt said.

Privlo, a self-described “alternative” mortgage startup in Pasadena, Calif., backed by venture capital, is leveraging technology to quickly ascertain the creditworthiness of borrowers based on a wider range of data than is typical, said Michael Slavin, the company founder. The company’s goal is to offer a pure online experience.

Economic changes since the recent recession have widened the pool of self-employed people who are not adequately served by the current lending market, Mr. Slavin said. “Corporations that went through vast layoffs are still outsourcing a lot of their talent,” he said.

He distinguished Privlo from subprime lenders, noting that “we take our underwriting very seriously and we retain ownership of at least a portion of every loan.”

Angel Oak Home Loans, a retail lender in Atlanta, is offering loans of up to $1 million under a program geared toward borrowers who have had an isolated negative credit event like a short sale or foreclosure.

The company will approve a fixed-rate loan less than a year after the event, if the borrower is able to make a substantial down payment, often around 25 percent, and has good residual income, said Steven Schwalb, the managing partner. “We want the responsible user who just got caught in a very tight, tight spot,” he said.