Annexing Puppet Cities?

When is it usually best to annex cities you've had as puppets? In my current game, I have 4 founded cities and 4 puppets. I've kept all my puppets as puppets for the purpose of building the most important national wonders. Now that I've completed the most essential national wonders, I'm wondering if I should start annexing some.

All four of my puppet cities have a religion that allows for the building of mosques and cathedrals with faith. So if I store enough faith, I could instantly build both a mosque and a cathedral in my newly annexed puppet; increasing happiness by one, culture by four and faith by five. just wanted to mention this, as I'd imagine it could effect the decision.

Thanks in advance.

For timing:

1. The city that you previously puppeted must have come out of resistance

2. It must not interfere with current or near future national wonder building

3. You should either have enough cash to rush a court house or alternatively the city already has a good enough production that when you take control it can build one in a few turns.

If for some reason you are only one or two turns away from finishing a cultural policy you might want to wait to finish those as well. (Similar to being very close to triggering a natural Golden Age)

If you are in golden age and wont go into negative happiness, that is a good time to annex, too. I usually dont annex at all, though.