This should be an easy one, but a Google search (and forum search here) turns up nada.
The artist sounds a lot like Lene Lovich, but with stripped-down arrangements. I wouldn't be surprised if it were one of Lene's later period songs, but I've scouted through her discog and couldn't find a match.
Here's the mp3. It's a pretty good 80's song:
<a href="https://www.yousendit.com/download/MFo1SXR3T01iV3l4dnc9PQ" target="_new">In My Sleep.mp3</a>
Here's a sample of the lyrics:
[b]In my sleep I go walking with you
In my sleep I'm never talking to you
In my sleep the faces look so mean
In my sleep the places look so clean
(chorus)
In my sleep, I'm watching sheep in my sleep...
In my sleep, I'm watching sheep in my sleep... [/b]