The Bush administration's decision last week to normalize diplomatic relations with Libya is - without doubt - an exercise in big-picture foreign-policy thinking.

The change will remove Libya from the "state sponsor of terrorism" list, lift economic sanctions, reopen a U.S. embassy in Tripoli after 27 years, end a travel ban and pave the way for American trade and investment. Congress has 45 days to object.

The decision isn't necessarily popular - or without controversy. Some victims' families of Pan Am 103, downed by Libyan agents in 1988, killing 270 near Lockerbie, Scotland, object strongly -- with good reason -- to bringing Libya in from the cold.

Libya's bad behavior doesn't end there. Tripoli also blew up a German disco (killing 3 Americans); invaded Chad; downed a French airliner; trained/financed terrorists (e.g., Black September), sent the IRA arms, pursued WMDs and befriended Liberian thug Charles Taylor.

And, yes, Col. Moammar Khaddafy, Libya's eccentric (to put it mildly) leader, is no democrat. In fact, watchdog groups often cite Libya, a military dictatorship of 6 million mostly ethnic Arab-Berbers, as one of the world's most repressive regimes.

So why reopen diplomatic relations with such a despicable regime? It comes down to significant, measurable progress on matters of great importance to U.S. interests.

Terrorism: In 1999, Tripoli began distancing itself from terrorism by surrendering for trial the Libyan agents responsible for Pan Am 103. Moreover, Libya agreed to a nearly $3 billion settlement with the victims' families. The first tranche of more than $1 billion was disbursed after U.N. sanctions were lifted in 2003.

Libya has since signed all 12 of the U.N.'s counterterrorism conventions, too. More important: It actively cooperates with us against al Qaeda and its affiliates in North Africa, including the Libya-based LIFG and Algeria's GSPC.

WMD: Libya has come clean on WMDs. In 2003, Libya began turning over its nuclear program to us, including uranium hexafluoride (enough for a small nuke), uranium enrichment centrifuges and engineering designs for a nuclear warhead.

Tripoli also dished on its dealings with A.Q. Khan, the CEO of Pakistan's nuclear Walwart. Khan shared Islamabad's nuclear know-how with Iran and North Korea, as well as Libya. Tripoli's cooperation proved critical in unraveling the network.

Libya has also begun taking steps to destroy its chemical weapons materials and munitions under international supervision. Plus, it's eliminating its SCUD ballistic-missile program and refraining from developing other longer-range weapons.

If swearing-off terrorism, WMDs and long-range missiles isn't enough, normalizing relations with Tripoli brings other benefits to American interests.

For starters, it encourages other rogue states to come in from the "WMDs/terrorism" cold. The clear message to Iran and North Korea: Abandon such policies, and you "will find an open path to better relations with the United States and other free nations," in the words of Paula DeSutter, a State Department official.

Perhaps equally notable: Libya's stark transformation demonstrates that the United States is (grudgingly) willing to live with a change in regime behavior as an alternative to regime change - every despot's and dictator's worst nightmare.

Then, too, Libya is a significant source of high-quality, light ("sweet") crude oil and natural gas. In fact, experts say that due to Libya's isolation, the full-extent of its oil reserves isn't fully known - further exploration could double today's forecasts. With today's oil/natural gas prices -- and the nasty energy power politics of Iran, Russia and Venezuela, plus instability in Nigeria -- putting another major source of oil and natural gas on-line is a real plus for America's energy security.

Resuming commerce with Libya would also open a long-closed market for other U.S. businesses, from aviation to telecom.

So, while the United States can't take any pleasure in recognizing the Libyan regime, it's a practical step for many reasons. And it doesn't mean we're likely to see the garishly-dressed Khaddafy welcomed on a Washington visit anytime soon. Libya must still clean up its act on human rights, liberalize its political system and economy - and steer clear of trouble.

The Bush administration - and its successors - must continue pressuring for change, keep a vigilant eye -- and remind Tripoli that the upswing in relations is fully reversible.

Peter Brookes is a Heritage Foundation senior fellow and author of the book "A Devil's Triangle: Terrorism, WMD and Rogue States."