The problems are not new.
More than a year ago, the County Council told then-Sheriff John Lovick's staff to rein in costs and provide regular progress updates.
That was after the jail went about $2 million over budget for 2012.
Yet on Wednesday, council members were again addressing a budget overrun.
"Just the enormity of it is a red flag, and these costs need to get under control," Councilman Terry Ryan said.
The $5 million figure is an estimate from at least a month ago; the full number won't be confirmed until February, when final accounting has been completed through the end of last year.
Ryan, who is in his first week in his county job, declined to pin blame on anyone, but said he wants the issue solved.
Councilman Ken Klein, also in his first week, asked whether the problems were likely to resurface.
"A big chunk of this is a one-time hit that obviously isn't going to reoccur in 2014," said Brian Haseleu from the county finance department.
Sheriff's spokeswoman Shari Ireton said the reasons for the rising costs are complicated and have been discussed openly for months.
Of the $5 million, $2.8 million stemmed from three new labor contracts signed last year. They covered sheriff's deputies, corrections staff and sheriff's office management.
Deputies have been working without a contract since April 2011, so the new bargaining agreement includes pay raises retroactive to that time. For corrections officers, raises go back to January 2012.
The other higher-than-expected costs mostly involve the jail: $785,000 for detention overtime; $430,000 for staffing the medical corrections unit; $420,000 to contract for outside medical services; and failing to meet a target to under-spend the available jail budget by $215,000.
The sheriff's office also paid out $350,000 because of higher-than-expected turnover among deputies, which required paying out accrued leave to departing employees.
County Executive John Lovick was sheriff until being appointed to the county's top job in June. Ty Trenary, a sheriff's captain, was appointed to succeed Lovick a month later.
To cover the overruns, the council took $3.7 million from reserve funds and transferred another $1.3 million from a fund for unexpected personnel costs.
The vote was unanimous.
"The overtime's been an issue for some time," Council Chairman Dave Somers said. "I spoke with the sheriff yesterday and reminded him it's a top priority to get this under control."
While agreeing that costs need to come down, Somers said problems involving inmate health care, to some extent, have been beyond the sheriff's control.
Early last year, Lovick requested an outside review of the county lockup following two high-profile deaths involving inmates who were both in their 20s.
This fall, a 100-page federal report identified a host of problems: inadequate staffing, overcrowding and a health policy in need of "comprehensive reform."
Ireton said those jail-related challenges are playing a big role in driving up expenses.
"We are doing everything we can to reduce the cost, but the bottom line is when the NIC (National Institute of Corrections) came in and did the assessment of our facility, one of the top recommendations they had was to reduce population and increase staffing," Ireton said.
The jail has made progress in some areas.
It has filled all openings for medical staff, including nurses and a doctor, who have been hard to recruit. That should reduce costs for outside health-care services. Even so, Ireton noted, the National Institute of Corrections said the jail's medical staff should be expanded beyond what's in the budget.
The original sheriff's office 2013 budget was $93.5 million. The jail accounts for just under half of those costs.
Law and justice costs have ballooned as a portion of county spending over the past two decades. Courts, police and related functions now eat up more than 70 percent of the operating budget, compared to just over 50 percent in 1990.
Noah Haglund: 425-339-3465; firstname.lastname@example.org.
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