Confusion in the defination of one unit of restriction endonuclease - (May/26/2010 )

I think there is some obscure in the defination of one unit of restriction endonuclease.
say"One unit of restriction endonuclease activity is defined as
the amount of enzyme required to produce a complete
digest of 1 µg of substrate DNA (or fragments) in a total
reaction volume of 50 µl in 60 minutes under optimal
assay conditions as stated for each restriction
endonuclease. "
Here is my question,there is no defination about the density of "restrction sites",say is there 1 or 10 or 100 of certain sites per kb of DNA above?Won't it make any different?
When it comes to the cut my PCR products,given that 10unit of nuclease X is needed per ug of DNA,but them didn't say how many cut sites are assumpted per ug/kb of DNA.
given there is one certain cut site per copy of my PCR molecue,if the size of my product reduce 10 fold,then the cut site number per ug/kb will increase 10 fold.Should I still add the same volume of enzyme?
Well,the real problem is I always got self-ligation of my double enzyme cutted vector.
Initially,EcoRI and BglII,then SalI and XhoI.
I can't determine if the activity of enzyme is compromised or there is some thing wrong with my operation.
I typically cut 2ug of vector with 1.5ul of enzyme each site in a 50ul volume and incubate over night.
I typically purified 4×20ul of PCR product,and cut them all in a 50ul volume with 1.5ul enzyme each.
Then I realize there is a huge mount of DNA in 4 tubes of PCR system,then I'm afraid the cut won't be sufficient.
what do you think?what is your habits?

normally the unit of a restriction enzyme is calculated/defined using a "certain DNA" as its substrate and is never based on "random or any DNA". if you read the insert accompanying the enzyme, you will clearly see that they have written there that wat DNA is used as a substrate to define the unit of enzyme. in most of the cases, lamda phage DNA is used. so it is always a certain DNA of specific length and containing a known number of cut sites which is used to define the unit of restriction enzyme.