From the ArcaMax Publishing, Gardening Newsletter:
http://www.arcamax.com/news/gardening/s-1895-394625
Question: What is the appropriate care for alyssum? Should it be cut
back after flowering? Will it bloom again?
Answer: There are annual alyssum and perennial alyssum plants. Annuals
generally grow just 3"-4" tall and provide profuse bloom. When the
blossoms fade you can shear the plants back and they will flower once
again. The flower colors are white, pink or purple. Annual alyssum
grows well in full sun to very light shade, in ordinary, well-draining
soil.
Perennial alyssum is a shrubby, low-growing plant. It blooms
throughout the spring and summer if you cut it back by one-third after
flowering. This alyssum thrives in full sun and average soils kept on
the dry side. It grows best in rock gardens, and looks terrific
cascading over stone walls. Flower color is yellow.