If you want a REALLY good example of how this can work, I can show you how you can save $2,500 on an F fare from LAX to SIN on Singapore Air.

Flights 29 and 30 fly between LAX and SIN with a stop en-route at Taipei. If you book LAX-SIN-LAX on those flights, it's approximately $8,500 (I forget the exact fare). However, if you book it on the same flights, but as LAX-TPE-LAX; TPE-SIN-TPE, it's $2,500 cheaper.

And when you check in at lAX, they'll check you all the way through to SIN.

It's all how you book it...