Many asanas seem to beg to be paired with other asanas; Shoelace seems to flow naturally, organically into the Swan. Twists easily flow from one side to the other. Straddle folding over one leg (aka Dragonfly) easily invites folding over the opposite leg, and then a final fold right down the middle feels very natural.
Some yang poses seem to be made for when we come out of yin poses: Down Dog feels so good after the Swan. And if you never really cared for Down Dog before, after five minutes of playing with the Dragons, you will quickly learn why the Dog is a yogi’s best friend. Down Dog after the Dragon can even cure atheism! 
Shallow postures naturally precede deeper postures. For example, if you want to work on back bends or stimulate the kidneys, you may wish to start with Saddle Pose.  After the mild back bend of the Saddle, try the Sphinx for a few minutes. Then move into the Seal. Finish this sequence with Child’s Pose for your forward bending counterpose.