some restriction enzymes need additional bases either side of the cut site and others do not.Check the New England Biolabs website for specific information.. Afew enzymes cut upstream or downstream of the recognition site which is not always also the cut site. It seems that some enzymes need to bind either side of the cut site before cutting can take place. Afew enzymes even need more than one cut site before they will cut at all. It is usually better if you want efficient cutting to add 3 or more random bases at the 5, end of a primer if you are going to amplify DNA then restriction digest the product but check your enzyme of choice at NEB before you design the primer

thnx..