But a new law may mean many will have to wait a year before they are eligible for foreign adoption -- something that may put them beyond the desirable age range for many potential parents.
International adoptions had been on the rise in Belarus. Nearly 2,500 children have been adopted by foreign families during the past decade.
But President Alyaksandr Lukashenka has strongly condemned what he calls the "sale" of Belarusian children abroad. As he sees it, the new legislation -- which went into effect 1 November -- will protect many children from potential exploitation and abuse at the hands of foreigners.
Deputy Education Minister Tatsiana Kavaliova said that abuse of adopted children -- and not only by foreign families -- is a constant concern.
"There was a case in Sweden, where the adoptive parents were abusive to the little girl," Kavaliova said. "The adoption was rescinded and the little girl was then adopted by another Swedish family. This happens with Belarusian [adoptive] families, as well. Every year, we rescind the rights of 4,000 sets of adoptive parents."
Many countries in the former Soviet Union have provisions aimed at keeping orphaned children in the country of their birth. Russia and other countries have specific terms during which orphans can only be adopted by parents in those countries.
Many observers defend such measures as protecting the rights of children to find homes in their native countries.
But critics say it extends the time many children spend in orphanages -- an experience that will make their transition even more difficult if and when they are finally adopted.
Russia is by far the biggest source of adoptable children within the former Soviet Union. The popularity of adopting Russian children was emphasized last summer when German Chancellor Gerhard Schroeder and his wife adopted a 3-year-old girl from St. Petersburg. Even Hollywood actress Angelina Jolie, who already has one adopted son from Cambodia, is reportedly looking to adopt a second child in Russia.
But Russian officials have become increasingly critical of foreign adoptions, which they say are prone to corruption.
Russian Deputy Prosecutor-General Vladimir Kolesnikov this week cited numerous cases of regional officials accepting large amounts of cash to facilitate adoptions to foreign families. He described adoption as a "profitable business" and said a child can sometimes be sold for as much as $50,000.
It's an issue that has put new emphasis on finding Russian homes for Russian orphans.
Yurii Kudinov is humanitarian aid director for Children's Hope International, a U.S.-based international adoption agency that has also been promoting domestic adoptions since 1999.
"Our first priority is to help the child back to its biological family, if it's possible," Kudinov said. "If it's, for example, [a matter] of financial needs, or some kind of situation when the child was lost during a war conflict, we try to help [get] the child back to its biological family. The second option is domestic adoption -- domestic foster families and domestic adoption. Only the third one is international adoption."
As Kudinov sees it, there are many reasons to promote domestic adoption. In Russia, where the population is undergoing a steady decline, keeping children in the country is a smart step demographically. It also simply means that more orphaned children will find loving homes.
Kudinov noted that that even China -- which leads the world in foreign adoptions -- has fewer children living in orphanages, due to an aggressive campaign to promote domestic adoptions, as well.
Are domestic adoptions preferable to international adoptions? Kudinov said definitely yes.
"Because the child has the same language, especially the older kids -- and I'm talking about kids over three years old," Kudinov said. "Because we don't need to change the language, we don't need to go far away. Because actually, this is a big stress, even for a child who's three years old, to go outside of the country and fly 18 hours to the United States and after to meet parents who don't speak their language. Of course, they switch to the new language very quickly, but it's still very, very different."
Groups like Children's Hope International are aiming to help Russia move away from its long-standing tradition of institutionalized care toward more individual, family-based solutions like domestic adoption.
But other former Soviet countries, meanwhile, are quietly paving the way for their orphaned children to find homes abroad.
Azerbaijan recently eased restrictions on foreign adoptions, despite a heated parliamentary debate that saw some lawmakers worrying that children could be sold into prostitution or slavery.
Under the new guidelines, Azerbaijani families looking to adopt are given no special preference over foreigners. In the past decade, fewer than 100 Azerbaijani children were adopted by couples in the United States. But that number now looks likely to grow.
Irade Musayeva is the chief doctor at a psycho-neurological hospital in Baku that is home to some 100 orphaned children. She said that no institution can ever take the place of a real family -- whether Azerbaijani or foreign.
"Nothing can replace the family's warm environment of love, even if it is an excellent state institution," Musaeva said. "It doesn't matter if it's the child's real parents or adoptive parents. That's why I say that if there is an adopting family in Azerbaijan, it should go to that family. Otherwise, it should go to an adopting family in foreign countries."
The highly emotional issue of adoption leaves no easy answers for critics on either side of the debate. The Belarusian crackdown on foreign adoptions may seem shortsighted to a hopeful family in the West. The continued outflow of Russian children abroad could be lining the pockets of greedy regional officials.
Even advocates of domestic adoption admit there is no sure way to protect those children from coming in harm's way -- as a recent case in Tajikistan illustrates. There, a woman was sentenced to a lengthy jail term for forcing her 12-year-old adopted daughter into prostitution.
(RFE/RL's Azeri and Belarus services contributed to this report.)