'Amame' - Spanish Ballad for Bachata

Would be really delighted if someone could help me here:
The song is sung in Spanish by a woman with an amazing, haunting voice.
It's a ballad but it has a Bachata-feel to it.

I am pretty sure the chorus starts with 'Amame..'.

I have found one song that sounds similar but it's like a fast, mashed-up version of it (and this one is sung by a bloke):
http://www.youtube.com/watch?v=-oWZ0fKCv2I&feature=related

Does anyone recognise the song I mean?
For those who dance at Mambo City (London) this was played frequently as the first Bachata tune in June and July.
 
Thank you very much everyone for the guesses!

SALSOLOGY, you are a gentleman, a scholar and a stud!!!
I am punching the air with joy here, THAT's the one!!
How on earth did you work out what I meant?!?

An Italian-Cuban band...I would have never tracked that one down. And I was wrong, the song is indeed a 'proper' bachata.
I suppose I was too focused on the girl I was dancing with ;)

Cheers again!!
 
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