Also check free stopovers. Last time I went to Europe, I needed to go to Amsterdam. It was about 200 Euros cheaper to go to Madrid, which would make sense as it is closer. But in this case I flew KLM, so via AMS to MAD. KLM's base is AMS, so you can get free stopovers. My frist stopover was 2 months, then 2 weeks to Spain, then another stopover of 3 days to organize my luggage for the way back to Brazil.
Let me repeat that, South America - AMS-MAD -AMS -South America was cheaper than just SA-AMS-SA. So two extra flights and 200 euros less per person.
I hate to burn more carbon than needed, but it gave us a great opportunity to visit friends in Spain and save while doing it.
Anyway, moral of the story: check other destinations, while passing through where you actually want to go.