I have tested out different shipping solutions from the US to Kyiv. Here are the results:
1)
FedEx. Expensive and get's stuck in Ukrainian customs.Paid about $100 to ship a large envelope. Local FedEx representiative did not deliver the package to the residential address in Kyiv. Recipient had to go to the customs office to get the package. FedEx Service Center in the USA admits they don't have a good local representative in Kyiv.
2)
UPS. Expensive but ok delivery. Paid about $100 to ship a small envelope with documents. Local UPS representative delivered on the door as expected in a timely fashion. However when calling up the recipient to arrange for delivery, UPS driver offered to just leave it outside the door despite that signature was required for the delivery. Recipient declined this option and delivery was made in a correct manner.
3)
US Postal Service Global Express Delivery - The Best!Shipped same size envelope with documents. Cost $29 and delivery time only 2 days longer than UPS. Local neighborhood post office in Kyiv did an excellent job! They called up the recipient to arrange for delivery and the postal worker did a thourough job checking the recipient's identification. (Nor FedEx or UPS did so). The recipient was impressed how professional Ukrainian postal service was handling the Global Express Delivery from the US.
Conclusion, I will only use the US Postal Service Global Express Delivery or Registered Mail when shipping to Kyiv. It will also save me money as well.
A piece of advice. Instead of spending a lot of money shipping gifts to the lady. Send her money instead and she can buy the handbag she really wants. The selection in Kyiv is excellent. She will have no problem finding a nice handbag on Kretchatyk
Send her a PayPal card in her name and fund it via your checking or credit card account and she will get her money via the local ATM or Bankomat as they say locally. Cost only $1 per transaction and the USD/Hryvnia exchange rate is good. I even gave my Miss 2 cards so she has a backup in case something happens to the first card. I guess I must be a good PayPal customer since I am being kept busy funding it all the time

But who's complaining, I am not