Being a web-developer (NOTE: Not Designer) by trade, I dont have excessive experience with moving and slicing, but I have done it in the past...
Usually I slice in Fireworks (Macromedia Suite) and then move the data across using the HTML Export command into MMS DreamWeaver.

Usually (in fact in nearly all situations) you will find that the slices are a bit 'off' and the tables are nearly always incorrect. Unfortunately, due to the copmlex nature of Fireworks-created websites, this is just what happens. Often, there will also be sections where Fireworks has just put in 2px wide 'spacer blocks' which are not only time-consuming to load, but also very heavy on code, which at the end of the day just seems to make EVERYTHING slower!

The Macromedia Suite is rather pricy, but there are quite a few OpenSource Options which you should be able to find via Google.

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Hope you get it right without too much hassle!
~Equinox