During the period Safaev was serving as the country's ambassador to Washington, the U.S. State Department added the Islamic Movement of Uzbekistan (IMU) to its list of terrorist organizations.
The IMU is blamed for insurgent attacks in Uzbekistan and Kyrgyzstan in 1999 and 2000, and Tashkent has long considered the group an enemy of the government. Getting its name added to the U.S. terrorist list was widely seen as a professional triumph for Safaev.
When he was appointed foreign minister in 2003, it was seen as a sign of Tashkent's desire to forge stronger ties with the United States.
But now Safaev has been removed, and relegated to a post as head of the parliamentary Foreign Relations Committee. Does the appointment of his replacement, Elyor Ganiev, mean Uzbekistan is readjusting its foreign policy yet again?
Some observers say yes. A commentary yesterday in Russia's "Vremya novostei" daily said the switch signals a new pro-Russia tendency in Uzbek policy. The paper writes that Karimov "isn't hiding the fact that his 'illusions' about cooperation with the West have evaporated."
Uzbekistan's new dominant foreign-policy trend, the paper predicted, would be economic relations.
Ganiev previously served as the head of the Uzbek agency for foreign economic relations. But not everyone believes that a minister's background can serve as a forecast of the policy ahead.
Muhammad Solih is the leader-in-exile of Uzbekistan's banned Erk opposition party. He told RFE/RL that no foreign minister has the power to significantly alter the country's foreign policy.
"Sodyq Safaev was not pro-Western. He is just a small part of the whole system. In comparison with politicians like Elyor Ganiev, Safaev is just a little more intelligent, a little more of an open-minded person with experience working with the West. This is the difference. But in terms of fidelity to Karimov's regime, Safaev and Ganiev are in the same group," Solih said.
Bahodir Musaev, an independent sociologist based in Tashkent, agrees. He told RFE/RL it is almost inconsequential who holds the foreign-minister post, since it is ultimately Karimov who determines what policy the country should follow.
"I don't think the replacement of Safaev with Ganiev will change foreign policy from a Western-oriented policy to a Russian-oriented one. Is Ganiev known for a pro-Russia stance? No. We don't have public politicians whose personal opinions differ from the opinions of the president," Musaev said.
Musaev said there is only one reason behind last week's cabinet reshuffle -- Karimov's desire to further consolidate his power. "I believe there is only one trend behind this -- one that will serve the strengthen the presidential institution and [Karimov's] personal power," he said.
Other reshuffles include the promotion of Rustam Azimov from deputy prime minister to first deputy prime minister -- a post that gives Azimov, who also serves as economy minister, direct presidential access.
The head of the Central Election Commission, Buritosh Mustafaev, also ascended to a government post, becoming justice minister.
Sociologist Musaev says Karimov reshuffles his cabinet often as a way of maintaining balance between different political clans. Azimov and Ganiev belong to one main faction whose members mainly come from Tashkent; Mustafaev belongs to another group, the Samarkand clan.
Musaev says the recent cabinet changes are of only minor significance, since top-tier politicians -- like Interior Minister Zakir Almatov -- remain in place.
"Currently, Almatov is one of the most influential figures [in the country], and he has not been replaced [for many years.] There is a huge force behind him -- the police. If Almatov was replaced, then we could definitely expect some changes in internal policy. There could be a softening of the repressive policy [of the Uzbek government]. But replacing Foreign Minister [Safaev] with Ganiev doesn't mean anything," Musaev said.
Observers say Karimov tends to demote those who become overly popular with the public, or the subject of speculation or gossip -- which is rife in politically opaque Uzbekistan.
Safaev had been a highly visible politician. And in 2003, rumors were rife that Safaev had married Karimov's eldest daughter, Gulnora. The story was untrue, but the rumor traveled fast, with the BBC among the first to report the marriage.
The Uzbek Foreign Ministry swiftly issued a statement denying the reports, spurring a flurry of allegations and denials that included speculation that Karimov had anointed Safaev his presidential successor.
Was Safaev's demotion last week a result of his connections with Washington? Did Karimov worry his foreign minister was a future Viktor Yushchenko or Mikheil Saakashvili to whom the West would turn to lead a democratic and free Uzbekistan? Sociologist Musaev says yes.
"The endless reshuffles aim to keep individual politicians from strengthening their positions and creating a corporate structure that would be separate from the presidential one," Musaev said.
With the latest reshuffle, both Musaev and Solih say Karimov has come closer to his goal of absolute presidential power. How he intends to use it, however, remains to be seen.
(Khurmat Babajanov of RFE/RL's Uzbek Service contributed to this report.)