She's not from my country, but UK artist Imogen Heap releases some wonderful music.

Neither is Björk Guðmundsdóttir (or more commonly known as Björk), but she's simply amazing.
Homogenic is a marvelous achievement in music.
Try some oldies. Paula Abdul (
Straight Up is pretty darn catchy) and Whitney Houston (
I Wanna Dance With Somebody) have some classics. Oh, and if you want something a bit more rock, give Janis Joplin a listen sometime. Her voice may not be everybody's cup of tea (it can get
very raspy), but I think she churned out some pretty good music.
Could you make a few exceptions? I think you're missing out on some pretty good music by male singers. Steve Burns (the host of
Blue's Clues) released an album a few years ago, and it's awesome.

Jack Johnson also has a pretty soothing voice; you might like his music.