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State data released this morning shows that unemployment is easing a bit, though at a painfully slow clip.

California's unemployment rate was 11.7 percent in May, down a bit from the 11.8 percent rate in April, and significantly better than the 12.4 percent unemployment rate in May 2010. Nationally, the unemployment rate for May actually increased, to 9.1 percent.

So California, as a whole, is still doing worse than the nation generally, but it is seeing improvement while other job markets continue to decline.

However, a state Employment Development Department payroll report found that, by that measure, California actually lost 29,200 jobs in May.

Only two employment categories in the state, the EDD found, showed gains: information and financial activities. The largest decline among job categories was in the amorphous "business and professional services" category.

The state data showed that San Francisco and some of the Bay Area counties are doing considerably better than the state average, likely reflecting the strength of SIlicon Valley and financial services here. The May unemployment rate for San Francisco was 8.4 percent. For San Mateo County, it was 8.1 percent. Santa Clara County was at 9.7 percent; Contra Costa County was at 10.3 percent; Napa at 8.7 percent; Sonoma at 9.4 percent;  Solano County was at 11.3 percent. Marin County had the lowest unemployment rate in the Bay Area, at just 7.4 percent.