You haven't heard Sam Phillips? You should. Born Leslie Phillips, she picked up the nickname Sam after the legendary producer of Elvis Presley. Her early Leslie Phillips records are Christian in nature, but definitely not of the "praise god" variety--she sings more of the heart than the head.
Her "middle period" records are where I first became familiar with her, and I defy you to find a more perfect pop record than The Indescribable Wow (which you can usually find used for a decent price; link provided for information only). Great compositions, stick-in-your-head melodies and that voice--unique. She followed that record with Cruel Inventions which deepened the sound without sacrificing its heart. I strongly recommend both of these to introduce you to her work.
Her two most recent records are more hushed and almost folk--Fan Dance and A Boot and a Shoe. Both are excellent, to the point records with no fluff. She had a couple of experimental records in between that paved the way for this direction; completists take note but otherwise, focus on these four records (and the Baroque Beatlesque Martinis and Bikinis which is a masterpiece of another sort). And enjoy.