To propagate Iris Laevigata, the most common method is to divide the rhizomes by carefully digging up the plant after flowering, then separating healthy, young rhizome sections with at least one fan of leaves, and replanting them individually in fresh soil; ideally, divide and transplant every 2-4 years to maintain plant vigor and optimal blooming. 

Key points about propagating Iris Laevigata:

Best time to divide: Late summer or early fall, after flowering is finished. 

How to divide: Use a sharp knife to cut the rhizome into sections, ensuring each section has a healthy fan of leaves. 

Discard any old, woody, or diseased rhizome parts. 

Planting new divisions: Plant the rhizomes with the top slightly exposed to the soil surface. 

Space the new plants according to the variety and desired effect.  Water thoroughly after planting. 

Important considerations:

Container culture: If growing Iris Laevigata in a container, repot every 2-3 years into a slightly larger pot with fresh potting mix to accommodate the growing rhizomes. 

Water requirements: Iris Laevigata prefers moist soil, so ensure consistent watering, especially during hot weather. 

Sunlight needs: Provide full sun for optimal flowering.