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It’s a weird-looking bird with a too-long beak and large eyes set high on its head, as if someone assembled it with spare parts.

But fans of woodcock admire the little robin-sized game bird for its distinctiveness and erratic dipsy-doodle flight — which makes shooting them on the wing so challenging.

And, despite a questionable reputation as table fare by some people, “timberdoodle” hunters also tout them as good eatin’.

“They are such unique birds, a shorebird that lives in the forest, beautiful, with their spring courtship sky dance,’’ said Tom Cooper, an avid woodcock hunter and wildlife biologist with the U.S. Fish and Wildlife Service’s migratory bird division in Bloomington. “I enjoy hunting them. They are tough to hit, that’s for sure.’’

Cooper rejects the notion they are unpalatable.

“They do have a bit of a liver flavor; I marinate them in Italian dressing and grill them,” he said. “The key is to not overcook. They’re pretty tasty.’’

Minnesota’s woodcock season opened Saturday and runs through Nov. 4. New this year: A federal change boosts the possession limit to nine birds, triple the three-bird daily limit.

While many ruffed grouse hunters will encounter woodcock in thick, young aspen stands, and will sometimes shoot them as “bonus’’ birds, hunters like Cooper specifically target timberdoodles, and view grouse as ancillary action.

The heavy leaf cover in September makes bagging woodcock even more difficult.

“It’s tough hunting the first couple of weeks,’’ Cooper said.

Hunters are shooting mostly local birds, but woodcock range far into Canada, and when they migrate through Minnesota — the peak generally is in mid-October — the action can be hot.

“I’ve seen 30 to 40 flushes in a couple of hours,’’ said Cooper, 42, who does woodcock research and helps compile the Fish and Wildlife Service’s national woodcock population status report. “Just like duck hunting, you have to be there when they are there.’’

A niche species

Until last year, an average of about 12,000 Minnesota hunters pursued woodcock annually. The estimated number of hunters hit 14,000 last fall, up from 10,000 in 2011 and the highest in 12 years. Those hunters shot about 32,000 birds, the most since 2009. Nationally, hunters bagged about 280,000 woodcock.

Steve Merchant, Department of Natural Resources wildlife program manager, said he has no explanation for the apparent 40 percent increase in woodcock hunters last year.

“I’m skeptical,’’ he said. The information comes from the DNR’s annual small game hunter survey, and he has asked his staff to review the data.

Regardless, woodcock hunters are a niche species, like their quarry. In comparison, there were an estimated 97,000 ruffed grouse hunters, 90,000 duck hunters and 84,000 pheasant hunters last year.

Population healthy, for now

Woodcock are found from Minnesota to the East Coast and from the Gulf of Mexico to southern Canada. Their population has been stable over the past 10 years, following a downward trend likely caused by a loss of young aspen, key habitat.

“Minnesota is one of the states we’ve actually had a stable trend since the beginning,’’ Cooper said.

Logging for the state’s forest products industry has created and maintained young aspen stands here. The birds feel safe in the thick cover, using their long bills to probe into soft earth for worms and bugs.

“Woodcock like the dense regrowth of the forest after disturbance, whether from fire or logging,’’ Cooper said.

Most of the woodcock moving through Minnesota spend the winter in Louisiana. One concern here is the recent decline in the state’s forest products industry, which could result in diminished habitat for woodcock and ruffed grouse.

Unraveling mysteries

Despite years of research, much isn’t known about woodcock.

“We don’t know a lot about their migration,’’ Cooper said. “How long it takes them to get from Minnesota to Louisiana, how many stops they make along the way and how long they stay at different staging areas.’’

Cooper and fellow researchers are experimenting with tiny GPS transmitters that they plan to affix to some woodcock this fall to answer some of those questions. “We’re testing the technology first,’’ Cooper said.

The transmitters, which weigh about 9 grams (about one-third of an ounce), use solar batteries.

“When the birds are in thick cover, we don’t know if they will get enough sunlight to charge them,’’ Cooper said. “It’s a long ways from being operational. But if it works, we will find out a lot about woodcock.’’

2013 woodcock season

Sept. 21-Nov.4

Daily bag limit is three and the possession limit is nine, a change from previous years.