By Andrew Cawthorne

CARACAS (Reuters) - Demoralized by their failure to unseat President Hugo Chavez, Venezuela's opposition hopes to bounce back in December state elections that provide a chance to curb the socialist president's power.

The opposition holds seven of Venezuela's 23 states and is fighting to at least keep those by appealing to voters' worries over uncontrolled crime, cronyism and sputtering services.

But the government is counting on momentum from the October 7 presidential election victory - where Chavez's charisma and anti-poverty programs outweighed weariness with those day-to-day problems - to make gains at a regional level.

Chavez carried all but two of the states in his re-election triumph and is now sending out some political heavy hitters inside his party to try and wrest control of some opposition-held governorships.

"No one is giving up," said Ramon Guillermo Aveledo, mastermind of the opposition Democratic Unity coalition that this year managed to unite Venezuela's diverse opposition parties for the first time during Chavez's 14-year presidency.

"The reasons for this struggle remain exactly the same," added Aveledo, urging supporters to ensure a good turnout despite disappointment at opposition candidate Henrique Capriles' 11-point loss to Chavez in the election.

Chavez's new six-year term starts in January and will extend his rule to two decades, though there is speculation the cancer that floored him for a year from mid-2011 may recur.

Opposition leaders generally stay quiet on Chavez's health but view the December 16 state elections as a chance to at least limit his influence.

Despite being squeezed of funding by the central government, most of the seven opposition governors have won plaudits for relatively efficient administrations. Capriles governs Miranda state and used his successes there in health, education and food programs as a springboard for his presidential bid.

Now he is locked in the headline battle on December 16, when he will seek re-election in Miranda and faces Chavez's high-profile former vice-president, Elias Jaua.

Promising to deepen socialist reforms and improve efficiency in his new term, the 58-year-old Chavez handpicked Jaua and is providing ample campaign resources to try and sink his presidential rival's political future.

"He's not going to have the Miranda governorship as a consolation prize," declared Jaua, 42, a former stone-throwing student radical who is one of Chavez's most trusted allies.

Capriles, 40, insists he is back in fighting shape and is reminding voters that, even though he fell short, the opposition had its best showing against Chavez, with a record vote of 6.5 million or 44 percent of the total.

"Who didn't have a cry on that Sunday? I was very down," he said. "But now I'm back on my feet, and will do all in my power to ensure we win a majority of governorships."

CHAVEZ FACTOR DOMINATES AGAIN

A good showing for the opposition would improve its power base, enable a new generation of leaders to have crucial experience in office, and potentially give them leverage in braking Chavez's policies at local implementation level.

A poor performance might reopen some of the internal dissent and splits that have plagued them in the past.

Bolstered by his re-election and his successful cancer treatments, Chavez is likely to hit the campaign trail to help Jaua and other government candidates for the governorships.

With the opposition traditionally doing better in local rather than presidential polls - which are a vote on the still-popular Chavez - the president's personal presence in the campaign is vital for his candidates.

Chavez acknowledged cancer radiotherapy treatment earlier in the year had left him weakened for the presidential bid. Health issues may again limit his role in the regional campaigns.

"I was boxing with my left hand tied up, and one leg tied up," he said last weekend. "This might sound arrogant, but if I'd been in top condition, I'd have won by 20 points."

Opponents hope that now that Chavez's place in the presidential palace is secure again, the December elections may turn into a protest vote against Socialist Party governors from an electorate unhappy over many grassroots issues.

A lower turnout than the record 81 percent of voters in the presidential election may also hurt Chavez's allies.

"You cannot compare the two votes," said pollster Luis Vicente Leon, who accurately predicted the presidential race.

"Chavez is not the candidate in these elections, the strength of his regional candidates is not equivalent to him and in these elections you get 10-15 percent fewer voters, two million people, which could radically change the game."

Another high-profile opposition leader, Pablo Perez, who was runner-up to Capriles in the opposition's February presidential primary, will be fighting to keep his post as governor in the oil-rich western state of Zulia.

Henri Falcon, 51, a former military ally of Chavez who broke with him in 2010, is seeking re-election in Lara state.

Chavez has reshuffled his Cabinet to send some of his most trusted allies into the regions to battle for him.

As well as Jaua, the outgoing ministers of interior Tareck El Aissami, indigenous issues Nicia Maldonado, and the presidency office Erika Farias are all contesting governorships.

Chavez's brother Adan will seek re-election in the family's home state of Barinas, in Venezuela's agricultural heartland.

(Additional reporting by Deisy Buitrago, Editing by Kieran Murray and Doina Chiacu)