Police say they are pursuing a "critical" lead in the Madeleine McCann investigation.
Metropolitan Police Assistant Commissioner Mark Rowley said four potential suspects had been ruled out.
But the new "significant lines of inquiry" are said to be of "great interest" to both the UK and Portuguese teams.
It comes a week before the 10th anniversary of Madeleine's disappearance from a holiday apartment in Portuguese resort of Praia da Luz in Portugal on May 3 2007.
Her parents, Kate and Gerry McCann, of Rothley, Leicestershire, have vowed to "never give up" hope of finding their daughter.
Officers have sifted through 40,000 documents and looked at over 600 individuals since 2011.
Asked if police were any closer to solving the case than they were six years ago when the UK investigation was launched, Mr Rowley said: "I know we have a significant line of inquiry which is worth pursuing, and because it's worth pursuing it could provide an answer.
"But until we've gone through it, I won't know whether we are going to get there or not.
"Ourselves and the Portuguese are doing a critical piece of work and we don't want to spoil it by putting tit bits of information out publicly."
He declined to expand on the nature of the working theories, or reveal whether any suspects were currently being considered, saying that disclosing further detail would not help the investigation.
Mr Rowley said: "We've got some critical lines of inquiry, those link to particular hypotheses.
"But I'm not going to discuss those because those are very much live investigation.
"We've got some thoughts on what we think the most likely explanations might be, and we are pursuing those."
He described the possibility of a "burglary gone wrong" as a "sensible hypothesis" which has not been"entirely ruled out".
The senior officer was asked about the theory of a sex predator being responsible for Madeleine's disappearance.
Mr Rowley said: "That's been one key line of inquiry. The reality is in the modern world in any urban area if you cast your net widely you will find a whole pattern of offences.
"You will find sex offenders who live nearby. And those coincidences need to be sifted out, what's a coincidence and what may be linked to the investigation that you are currently doing.
"Offences which may be linked have to belooked at and either ruled in or ruled out."
Mr Rowley said there was still a "lot unknown" in the case, adding: "All the different hypotheses have to remain open."
Meanwhile, police working on the case continue to receive information on a daily basis.
Mr Rowley said: "Thousands of pieces of information have come forward, some useful, some not, but amongst that have been some nuggets that have thrown some extra light on the original material that came from the time.
"That's one of the things that's helped us make progress and have some critical lines of inquiry we want to pursue today."
Mr Rowley said there was no "definitive evidence" as to whether Madeleine is alive or dead.
He added: "That's why we describe it as a missing person inquiry. We understand why, after this many years, people will be pessimistic, but it's important we keep an open mind."
Last month the Home Office confirmed £85,000 was being given to the inquiry to cover operational costs from April to September.
More than £11 million has been spent on the inquiry so far.
Mr Rowley insisted the investigation has achieved "an awful lot".
He said: "I think people get seduced perhaps by what they see in TV dramas where the most complex cases are solved in 30 minutes or 60 minutes. What we started with here was something extraordinary.
"We've achieved a complete understanding of it all. We've sifted out many of the potential suspects, many of the people of interest and where we are today is with a much smaller team focused on a small number of remaining critical lines of inquiry that we think are significant."
Asked about the cost of the investigation, he said: "Big cases can take a lot of resources and a lot of time.
"We've tried to be careful about public money and as we've started with that massive sifting we've reduced the number of resources and the funding's reduced accordingly.
"But we will stick with it as long as the funding's available and as long as there are sensible lines of inquiry to pursue."