CLAYTON, Mo. » On a typical recent morning Colleen M. Polak, a St. Louis County public defender, ran upstairs and down and up again and in and out of four courtrooms, simultaneously representing clients in 10 cases. She consulted, negotiated and sometimes just waited.

On this day, one client was sentenced to six years for illegal gun possession after a judge dismissed Polak’s objections to what she called questionable evidence. Polak, 32, was disappointed, saying that she had spent weekends on the case so as not to deprive other clients of her time but that it was impossible to spread herself as thinly as the job required.

"Some clients are probably not getting as much attention as they deserve," she said. "That’s what bothers me the most."

More than a half-century after the Supreme Court ruled that impoverished criminal defendants must be provided lawyers free of charge, the state of indigent defense remains "unconscionable," in the words of Attorney General Eric H. Holder Jr.

Here in Missouri, where public defenders say they are especially burdened, many legal experts hope that an exhaustive new analysis of workloads and needs, sponsored by the American Bar Association, will strengthen their multiyear battle for change.

Chronically understaffed, and reeling from caseloads several times larger than those managed by private lawyers, public defenders here and in many parts of the country have started trying to force legislators to respond. In the past two years, defender agencies in Missouri and Miami have won, in state Supreme Courts, the right to refuse new cases they cannot responsibly handle.

Case refusal, with its potential to disrupt court dockets and even force prosecutors to drop charges, has not yet happened on a large scale. In Missouri, prosecutors and some judges have challenged the need for it, arguing that public defenders are inefficient and no more loaded by work than other parties in the justice system.

But many other legal experts say the daily triage required of public lawyers is unconstitutional and forces them to violate their ethical obligations to clients.

"Limited resources move to higher-level cases like murder and rape, and thousands of other defendants are simply being thrown under the bus, with the illusion of a lawyer," said Stephen F. Hanlon, a private lawyer who is the chairman of a national bar association advisory group on indigent defense and who provides legal representation to the Missouri State Public Defender System.

The new report, described by legal experts as the most detailed and credible of its kind, has provided numbers to back up the claim that defenders here face Sisyphean workloads.

For the study, carried out in 2013 by the accounting firm RubinBrown, the 375 lawyers in the Missouri State Public Defender System recorded how they spent their time in five-minute increments.

Independently, a panel of private and public lawyers estimated the average time a defense lawyer in Missouri needed to properly argue cases of varying severity, including duties usually shortchanged by public defenders such as consulting with the defendant, investigating evidence, conducting depositions and researching legal options, as well as their time in court.

"We found we are worse off than we thought we were," said Cathy R. Kelly, director of the state public defender system.

For serious felonies, defenders spent an average of only nine hours preparing their cases, compared with the 47 hours they needed, the study found. For misdemeanors, they spent only two hours while 12 were called for.

Miami defenders last year also won the right to refuse excess cases. Carlos Martinez, the public defender for Miami-Dade County, said they had not yet done so because they want to complete a study like the one in Missouri first, and the caseload has eased somewhat in the past year.

In part, the decrease in cases reflects reforms in Florida’s juvenile system, which is sending fewer children to court. It also appears to reflect a decline in the number of police officers in many localities because of the recession, Martinez said. As hiring resumes, he said, "I think we’re going to see an uptick in arrests in the next two or three years."

In recent months, criminal referrals to the public defenders in Missouri have also dipped, apparently because prosecutors are filing fewer cases involving low-level drug offenses and probation violations, said Stephen Reynolds, chief of the St. Louis County Public Defender’s Office in Clayton.

"Until recently, lawyers here were carrying more than 200 felony cases, from drugs to rape and murder," he said. "I don’t think there’s any attorney who can handle that, no matter how good you are."

The burden has eased but is "still more than we can properly handle," Reynolds said.

Translating the bar association report’s numbers into staffing and budget, the state defender office has requested a funding increase of about $25 million, phased in over four years, to allow the hiring of 206 more lawyers and, crucially, 412 more clerks and investigators. It has requested an additional $4 million, among other increases, to cover about 4,000 cases annually in which juvenile offenders receive no representation.

But as he juggles budget priorities, Gov. Jay Nixon, a Democrat, has endorsed only a small fraction of the requested increases. In hearings so far, legislators have expressed appreciation for the new data in the bar association study, Kelly said, and she hopes the requests will gain support as the budget process continues into May.

What will happen if well-documented needs for indigent defense continue to go unmet?

"That’s the million-dollar question," said Douglas A. Copeland, a private lawyer and chairman of the Missouri Public Defender Commission, which oversees Kelly’s office. It is possible, he and others said, that judges may have to dragoon more private lawyers into providing defense without pay, or push district attorneys to drop less pressing cases, as it appears some are already doing on their own.

In the meantime, Copeland said, "I’m concerned that younger attorneys have never known anything different."

"They may assume they’re doing all they should for a client, when they really aren’t," he said.