tinyint is one byte, smallint is 2 bytes. Review how many values you can have for each (256 and 65K+ respectively) and use the right one for every dimension.
I support this concept, but at least in SSAS 2005 the tinyint can't be made into a connection in the DSV. So I avoid it even if it would have been a good choice. For those, the smallint isn't much of an increase and allows you to use negative numbers for the Unknown and (if needed) Not Applicable Bucket.