By Chris Hogg
BBC News, Tokyo
Should Japan build its own nuclear arsenal?
And should Japan's government rewrite the country's pacifist constitution to make it easier for its troops to be deployed abroad?
Each of these difficult questions has the potential to unsettle Japan's neighbours.
And yet senior politicians have been saying Japan needs to have serious debates on both.
Nuclear weapons have long been a taboo subject, but the need for a discussion was raised by a senior member of the governing party, Shoichi Nakagawa, in the aftermath of North Korea's nuclear test in October.
The Foreign Minister Taro Aso made similar remarks.
That prompted the new Prime Minister, Shinzo Abe, to make quite clear his government's commitment to its three non-nuclear principles - that Japan will not create nuclear weapons, possess them or allow them on Japanese soil.
You would have thought that would be the end of the matter.
But pressed in parliament this week by the leader of the opposition, Mr Abe appeared to indicate that discussions on nuclear arms should not be stifled.
"I think it would be going too far to say that there can be no debate at all," he said.
What's going on here?
According to the US Ambassador to Japan, Thomas Schieffer, Japan has benefited from being under the US "nuclear umbrella" for more than 50 years.
"I do not believe there is a strong movement here in favour of nuclear weapons. If the (US-Japan security) alliance was wobbly you would have a whole different concept. But the alliance is very strong," he said.
Yet an admittedly small number of Japanese politicians are still raising the issue.
N Korea threat
Political analysts say there are two ways of looking at this.
Conspiracy theorists say the prime minister is not worried that senior members of his party are talking about a Japanese nuclear deterrent.
Opinion polls show that more people feel threatened by North Korea than did before its nuclear test.
So by raising even the remote prospect that Japan should start to think about whether it needs nuclear arms to protect itself, the government is in tune with the popular mood.
The problem with this theory is that for years the polls have suggested that public opinion in Japan - the only country ever to be bombed with nuclear weapons - is resolutely opposed to building its own nuclear arsenal.
So there is another theory - that Mr Abe does not yet exercise as much authority as he should over members of his own party.
If that is the case, it does not bode well on the question over whether Japan should change its constitution.
The government argues that the current document - which was drawn up for Japan under the Allied Occupation after the end of World War II - is out of date.
Japan has the world's fourth largest military budget in dollar terms, and yet the constitution says it should not maintain armed forces.
As a result, as one analyst characterised it, Japan maintains the world's most expensive police force. The Japanese Self-Defence Force, as they are styled, have never fired a shot in anger.
Among the changes to the constitution proposed by Mr Abe is a new clause which permits a force, under the control of the prime minister, which defends the nation and may participate in international activities such as peace-keeping.
"What Mr Abe is trying to do on one level is just to change the constitution so that it accepts the situation that Japan is in now," according to Professor Phil Deans from Temple University in Japan.
But the technicalities of constitutional reform are very difficult. Mr Abe would need a two thirds majority in both houses of parliament and then a majority in a public referendum.
Will North Korea's actions make that easier or harder to achieve?
"The nuclear crisis may suit Abe because he'll be able to exploit that to get public opinion towards a position that says Japan must play a higher role," says Prof Deans.
"But it might work in the other direction too. It might send a signal to the Japanese people that the international environment is dangerous, it's frightening, and that the constitution offers the best protection for the Japanese to stop them getting involved in difficult overseas matters."
If Mr Abe is struggling to maintain party discipline, then embarking on such a debate could be risky.
Yokio Okamoto, an adviser to two former prime ministers, offered this advice.
"There are a lot of things Mr Abe could do, short of changing the constitution. There are a lot of legal challenges we can introduce to allow for instance Japanese forces to engage in peace keeping operations like those in Iraq" he said.
And yet the Prime Minister made clear in a newspaper interview last week that he wants a new constitution in place before he leaves office. And the longest he could serve under party rules is two terms, or six years.
So the question is, does he have the authority to push the debate on the constitution in the direction he wants it to go?
Pundits will be watching closely what happens over the nuclear issue to see what it tells them about his chances of success.