An attorney for the long-time girlfriend of James “Whitey” Bulger asked a federal appeals court in Boston today to recalculate her sentence for harboring the notorious gangster during his 16 years on the run, saying she was wrongly punished for being associated with him.

Catherine Greig, who stayed with Bulger for most of his time on the lam, pleaded guilty in June to conspiracy to harbor a fugitive and conspiracy to commit identity fraud.

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US District Court Judge Douglas P. Woodlock sentenced her to eight years, a sentence far more severe than she anticipated, based partly on what she had done to help Bulger remain one of America’s most wanted criminals.

The judge also considered the input of family members of Bulger’s alleged victims, who argued that she should be punished for helping him remain free for so long.

But Greig’s lawyer, Dana Curhan, told the US Court of Appeals for the First Circuit today that Woodlock erred in calculating the sentence under federal guidelines, and that Greig should have faced only 27 to 33 months.

Curhan said Woodlock spoke appropriately when he said last year that “there was no other harboring case like this.” But he said the judge erred when deciding on the sentence.

At the center of the argument was Woodlock’s finding that Greig not only harbored Bulger, but that she helped him remain in hiding by using fake identifications to buy medicine and groceries, and to pay rent. She also used Bulger’s cash, money she might have known came from his criminal activities.

Woodlock weighed that finding – as well as other issues, such as a conclusion that Greig lied about her finances – in calculating the sentence.

Curhan argued that Woodlock could not weigh what Greig did to help Bulger stay on the lam, unless she did things that were illegal, such as robbing a bank.

But Curhan seemed to find little support from the judges, who noted that Greig was convicted of identity theft, and that there was no denial that she bought the medicine and groceries for Bulger.

“This isn’t mere overnight sheltering of someone who ran in,” said retired US Supreme Court Justice David Souter, who often sits on the panel.

Appearing for US Attorney Carmen Ortiz’s office, First US Attorney Jack Pirozzolo argued that Greig’s level of culpability was increased by her work to help Bulger by obtaining his medication and paying rent for their apartment.

“That was considered something that went beyond the mere harboring of a fugitive,” he said. “That assists him in remaining concealed from law enforcement.”