The Danish diplomat will need to prove to skeptical local actors that the United Nations can credibly guide Kosovo through reforms in the aftermath of the worst ethnic violence since 1999. He must try to revive the dialogue between Belgrade and Pristina at a time when local Serbs are threatening to boycott the October provincial elections.
Jessen-Petersen also needs to find a sustainable way to safeguard minority rights, an issue his predecessors could not resolve.
At the same time, UN officials face calls from some UN Security Council members and nongovernmental experts for decreasing the size and scope of the Kosovo mission. Top UN officials are currently weighing a possible shift in strategy involving the transfer of more authorities to local bodies.
One of the UN's sharpest critics in recent months has been the Brussels-based International Crisis Group, an independent conflict-prevention organization. It has been in the forefront of groups calling for more clarity on Kosovo's final status, saying UN rule is now hindering more than helping the development of the province.
Nicholas Whyte, director of the group's Europe program, tells RFE/RL that the UN's bureaucracy is to blame for a failure to provide even simple services.
"Infrastructure such as electricity and water actually run slightly worse than they did under Serbian rule. There are real problems, and the UN hasn't made itself look as if it's a credible international administrator in Kosovo in that respect," Whyte said.
The UN operates under the mandate of Security Council Resolution 1244, which puts it in charge of areas such as police and courts, setting economic policy, and controlling power and telephone services.
The March outbreak of violence involving attacks by ethnic Albanians against Serbs and other minorities has focused attention on UN security shortcomings. But Whyte and others say the UN's biggest mishaps have been in running the economy, particularly privatization.
An article in "The Wall Street Journal" newspaper earlier this month called the UN-run privatization program a "showcase for the difficulties and dangers of trying to heal a fractured society through a lumbering international bureaucracy."
Privatization problems could be at least partly responsible for the province's high unemployment rates, especially among youth. Whyte says the UN's reluctance to hand over responsibility for economic matters to Kosovar Albanians has led to a breakdown in trust between the two sides on such matters.
"It would be a different matter if the UN was manifestly more competent in running this side of affairs than the local actors were, but that actually isn't the case. The UN economic pillar has been a byword for incompetence and corruption more or less since its creation," Whyte said.
A spokeswoman for the UN mission department in charge of reconstruction and economic affairs in Kosovo rejects Whyte's charges.
On the question of infrastructure, spokeswoman Katja Wallrafen says the amount of water supplied to the region of Pristina has increased 30 percent since 1999 and many rural villages are connected to a water network for the first time. Wallrafen says power production has increased by 25 percent in the province since 1999.
Whyte later amended his comments about incompetence and corruption in the UN economic pillar, writing to RFE/RL this week that his original comments were too strong.
But Whyte added: "It's undeniable that the UN economic pillar has a serious, long-standing image problem with regard to allegations of incompetence and corruption."
Wallrafen tells RFE/RL that the UN-run Kosovo Trust Agency is moving forward with a third round of privatization and is preparing for a fourth round.
There is a 15 September deadline for bidding in the third round on 13 companies, including a large metallurgical complex, printing plants, and a bottling plant. The UN agency had suspended the privatization process after two rounds in October 2003 because of concerns about its legality.
The privatization process is complicated by the unresolved status of Kosovo and whether or not it will remain part of Serbia.
Daniel Serwer, a Balkans expert at the U.S. Institute for Peace and a former State Department official, says that, regardless of the status question, the provisional institutions of self-government should be put in charge of the process.
He also says more effort should be made to hand over security responsibilities to ethnic Albanians.
"The UN has to not just be leaner and tighter and better run, it has to surrender authority over everything it can possibly surrender authority over. It has to stop worrying about whether the provisional institutions of self-government are going to make a mistake. They have to be allowed to make mistakes, because that's how people learn things. Now, there are limits in [Resolution] 1244 on how much authority can be turned over -- especially in the security area -- but within those limits there's a great deal that can be done by way of bringing Albanians into the process of law enforcement," Serwer said.
Such proposals are likely to arouse strong opposition from Kosovar Serbs and officials in Belgrade. They note that more than 2,000 Kosovar Serbs remain displaced by what was regarded as an ethnic cleansing campaign in March. Overall, nearly 200,000 Kosovar Serbs cannot return home out of fear for their safety.
Serbs have called for the creation of pockets of self-rule in Kosovo.
But there is clearly support among some key Security Council members -- such as the United States and Britain -- for accelerating the handover of some authorities to ethnic-Albanian-led institutions in Kosovo, while maintaining pressure for key reforms.
There are signals that a report recently commissioned by UN Secretary-General Kofi Annan may be heading in that direction. The report by Norwegian diplomat Kai Eide has not yet been released.
Council diplomats briefed on its contents say it recommends adjustments in the "standards before status" policy that could provide a more rapid devolution of powers to ethnic Albanian authorities.
UN officials are saying very little about the Eide plan, which has been shared with Serbian and Albanian leaders. UN officials have not signaled when they will make formal recommendations. A UN spokesman, Ari Gaitanis, would only affirm that it may contain some policy changes.
"I think that, hopefully, the Eide report will somehow maybe go some way to addressing the issues and concerns of the NGOs as well as any other parties involved in Kosovo," Gaitanis said.
Whatever the mechanism, it appears clear that the secretary-general's office will attempt to revive efforts to improve the treatment of minorities to maintain the goal of a multiethnic Kosovo.
Serwer, of the U.S. Institute of Peace, says resolving this issue will take better coordination of U.S. and European positions and more political will from Belgrade and Pristina, in addition to a more flexible UN approach.
"The only thing that stands in the way of a discussion of final status is the treatment of the Serbs and other minorities, and frankly this is not a matter of getting a few dozen people back to their homes and saying, 'Look what we did.' This is a matter of changing the atmosphere and the environment in which minority Serbs and other minorities are living in Kosovo, from one that is quite hostile all too often to one that is, at least, one of indifference, if not of welcome," Serwer said.
The standards-before-status policy, of which minority treatment is only one benchmark, was due to be reviewed in the middle of 2005.
That review is supposed to help determine when decision-making on Kosovo's final status can begin. Security Council Resolution 1244 calls for the respect for Belgrade's sovereignty in the province while also giving local institutions undefined powers.