Stay in each purvatanasana for three breaths but vashitasana for three to six breaths,
The challenge is to raise the hip(s) a little further on each exhalation.
As well as exercising the full range of the motion of the hip (along with the forward bending postures subroutines above) these postures are excellent for exercising the front back and side muscles of the legs that cross the knee joint. Exercising these muscles will give more support to the knee in the On one leg subroutines but also to advanced postures in which the knees are heavily involved.
Towards the end of Ramaswami's Complete book of Vinyasa yoga there is a chapter tittled Visesha Vinyasa Kramas, the sun salutation sequence with mantras is found here along with some other dynamic sequences. One of these sequence based on Vashitasana incorporates purvotanasana and vashitasana above but also the ardha-baddha padma vasitasana or Kashyapasana from Asymmetric. I thought it might be interesting to look at the full sequence here and especially at the last eight postures that pass back and forth between purvatanasana and vashitasana, it's a mini sequence I like to practice after the above postures.
Here's a link to a video of the short vasishtasana sequence http://youtu.be/fA4FHPTxSlg
And here's the full sequence. We are encouraged to stay at each stage for three breaths, it's a tapas sequence that I find makes a nice short evening practice to burn off a few of the days rajas before settling down to some pranayama and meditation.