Assigning vertex groups to bones precisely I've looked at several answers to this question and none of the responses are giving me what I need. 

Vertex groups are selected in the armature options, the vertex group names  correspond to the bones I want them to be attached to, and I parented the armature to the mesh with the 'armature deform' option (I tried automatic weights and the result was even worse). 

I would have thought that the vertex groups would be influenced 100% by the bones sharing the same name as the vertex group, and 0% by the bones that do not have the same name. 

This is not what is happening, as can be seen here: 



The 'base' bone influences the 'base' vertex group fine, but also influences the 'lid' vertex group -which I don't want. Furthermore, the lid vertex group looks like it is only 50% influenced by the lid bone, as shown here: 



I know there is an obvious remedy to this, but it's one I don't like using. Weight painting is not precise and very fiddly.
Fast and easy way to do it is in edit mode, select the part of the mesh that you want to be effected buy one bone, then in vertex groups select the group of related bone and assign weight with value of 1.

Then select other other vertex group and hit remove button.

Then repeat the same process on the other part of the mesh assigning or removing weight that you want to be associated with that part of the mesh.