Thanks for the reply.
That's great that it brings the attributes across, but not so good that it assigns a new value for each unique combination of input values in the output raster.
I've got a raster that I've created with the Fuzzy Overlay tool, and I can convert that to integer and I want an attribute table that states what each of the inputs are into the fuzzy overlay, so I guess each object in the raster attribute table will have a value for each of the inputs that went into making it. Fuzzy Overlay obviously doesn't bring this information across, but I thought if I could do some sort of intersect or spatial join, I could capture all the attributes for the other layers.
I get an error 'Too many unique values' when doing the combine anyway.