Fill a vase with warm (110 degrees Fahrenheit) tap water. Dissolve a powdered floral preservative in the water.
Cut the bottom inch from each bupleurum stem with a sharp knife. Make the cut at a 45-degree angle to provide a larger surface for water uptake into the stem.
Trim off any leaves along the stem that will sit below water level in the vase. Remove the leaves flush with the stem.
Set the vase in a cool (40 to 60 F) location for two hours. Cool air temperature combined with warm water encourages maximum water uptake by the flowers, resulting in a longer-lasting arrangement.