Double restriction digest

[Rick00100]

Hi Folks,

I'm trying to subclone a fragment into my vector.  I cut my vector with 2
different restriction enzymes to create sticky ends.  The problem is that I got
a lot of false positive transformants (after ligation to th efragment, of
course).  I think it is because the vector was not cut completely, and I
transformed a lot of the nicked vector to E. coli.  So my question is:  how do
you make sure the vector is cut completely by 2 enzymes? 

Thanks,
Rick