The country we are most intrigued by is Ukraine.
Adoption is different there in several important ways.
First, you are not allowed to use an agency in Ukraine. This is meant to eliminate a potentially corrupt middleman and to discourage human black market style transactions. You can hire a translator, or facilitator, but that's it.
Second, photo-listings of waiting children and pre-selection of any kind are illegal. This is also supposed to stop human traffickers and pre-bribing somebody to get a particular child.
Third, unless there is a health issue, children are kept in the system unavailable to foreigners for one year from the time they are documented.
I respect Ukraine for doing what it can to avoid immoral practices in adoption, but I can see a couple of potential deterrents for me here.
On the day that you are finally given your appointment with the state-run agency, you are shown books full of photos of waiting children and are expected to choose a few to enquire about within about an hour. The agency then calls the child's orphanage to confirm they are available (some of the files are old) and that nothing drastic has changed about their situation. If the child is sicker than the file indicates or if a long-lost relation has resurfaced, you may have to move on to another face.
If it looks like a potential match, you are sent on a trip to the orphanage. Some are a long way (17 hours in a decroded train) away. Sometimes when you reach your destination, other children are brought to you first, and may recite poetry or sing. If your heart hasn't shattered into a surprisingly small and black mess on their Eastern Block floor at this point, you may then see the child you selected from the books full of children. You have some time to consider the child and may visit several days in a row before announcing your decision.
The whole thing is wrapped up by a little more paperwork (am I signing up for another doctorate here?) and then you are officially family. Sometimes people don't find their child on the first few tries. You are allowed two appointments with the main agency, after which you are sent back to your country to recover and then may ask for one more appointment. Most people find their kids on the first trip, but others don't. With travel expenses and application fees (to the Embassies while you're filling out a year's worth of forms) most can expect to pay between $10,000-20,000. These fees also help defray the cost of the care the child receives while they are in the system, but are payed whether the parents travel home alone or not.
I respect the intent and think it's one of the best attempts at fairness I've come across. I just don't like the Jeopardy-timing parade of kids in need. That would take a LOT of prayer...
It's a system.