But it has taken on new urgency after the 24 March revolution. That's because many are concerned that existing legislation does not prevent the new president from gaining absolute power -- and becoming as authoritarian as ousted President Askar Akaev.
Seeking to take advantage of the current window of opportunity, the new Kyrgyz leadership established the Constitutional Council on 25 April. The council, holding its first session today, is an ad hoc advisory body due to be dissolved after the constitutional amendments are made.
However, the country's new leaders are already locked in dispute. They appear to have no consensus on what amendments should be made or how much authority to accord to each branch of government.
Many say the parliament must be given more authority. But not everyone supports the idea of changing from a presidential to a parliamentary system of governance.
Interim President Kurmanbek Bakiev, a favorite in June's presidential polls, supports constitutional reform. But he says the constitution must give broader powers and at the same time more clearly defined responsibilities to the president:
"The authority of a nationally elected president has to be greater because he is elected by the whole Kyrgyzstan nation," Bakiev told RFE/RL's Kyrgyz Service. "At the same time, a nationally elected president should have his [proper] responsibilities as well. For instance, the existing constitution does not design [the responsibilities of the president]."
However, Bakiev's main rival Feliks Kulov, the leader of the Ar-Namys (Dignity) party, says the legislature must be given more power.
Iskhak Masaliev, a Communist parliamentarian, says he supports this idea: "Our party's position has always been that Kyrgyzstan should be a parliamentary republic. We've had a presidential republic for 15 years. But we must not continue this way. I believe parliamentary form of governance suits us better."
In its first session, the Constitutional Court was expected to hear arguments of all sides as it seeks to identify which amendments to put to parliament for further discussion.
Omurbek Tekebaev, a long-time opposition leader, heads the council, which includes representatives of the government, the parliament, the judiciary, and civil society.
For his part, Tekebaev says he believes it's too early for Kyrgzystan to make radical changes in its form of government.
"I think it's too early for us to switch to parliamentary form of governance in its classical meaning," Tekebaev says. "Adopting the typical form of a European parliamentary republic would be a serious mistake for us. Our parliament would look like an [Oriental] bazaar."
Still others note that even a perfectly democratic constitution cannot on its own ensure that all branches of government will follow it. Many Central Asian countries, after all, have constitutions that meet international standards yet are often violated or amended by those in power.
Analyst David Lewis, director of Central Asia project of the International Crisis Group, says he believes Kyrgyzstan needs to try to better balance its governmental system.
"The idea is to produce more checks and balances within the system," Lewis tells RFE/RL by telephone. "The existing system does give a huge amount of power to the presidency, particularly in the area of appointments and in terms of things like control of the judicial system. So, I think the constitutional reform will also look at the judicial system, which has never been independent, and try to make it stronger and more independent in a new system, which will provide another check or another balance on the executive power. There is a very difficult equation and certainly constitutional reform is not a panacea. It's one step in a wider process."
Zamira Sydykova, editor in chief of "Res Publica" daily, agrees that the political system must provide better guarantees that the government will respect the constitution.
"It's necessary because without amending certain articles in the constitution, there is no guarantee that some gentlemen's agreement between different branches of power won't be broken," Sykykova says. "At present, the parliament doesn't have the authority to control whether the government follows laws or not. That authority was abolished by the two previous referenda."
Another concern of constitutional reform is its possible impact on clannishness of the political system of Kyrgyzstan.
If parliament is given more authority, will that result in more opportunity for each clan to participate in politics? Or will it deepen the division of the society into various clans?
Analyst Lewis says he believes the presidential form of governance deepens such divisions.
"One of the concerns about the powerful presidency is that it divides [Kyrgyzstan] into north and south. Because there is so much power in the presidency, regional groupings want to control that office," Lewis says. "At the moment, you have two major candidates for presidency -- one from the north [Kulov], one from the south [Bakiev], and it is expected that voting will divide along those lines. If the president is not so powerful, you won't have so much regional competition around that post. And regional interests can be represented much easier in a parliamentary system than in a purely one-person presidential system."
However, Lewis says a purely parliamentary system could also fuel regional competition if deputies are elected from single-mandate constituencies under a majority system.
That's how the current Kyrgyz legislators were elected, and the result was a parliament divided up into regional blocs.
It's still unclear just how and when any amendments should be adopted.
Some politicians insist on adopting them before the presidential election to ensure that the new president can't change them. But others say the amendments should be adopted in a referendum that cannot be called by the interim president and therefore must be held after 10 July.
(RFE/RL's Kyrgyz Service contributed to this report.)