The Desert Firetail is a tiny slender damselfly that ranges across the southwest from Texas to California and all the way south to Venezuela. The brilliant red of the male contrasts with the soft brown of the female. Their flight season in the U.S. is from March to Dec, but will vary by area. After mating they remain in tandem while she deposits the eggs on surface vegetation of warm ponds or creeks (duckweed, algae, etc.). Once you change your search image to "tiny" the red body of the male stands out well against the green vegetation (pond scum), even in flight. Beautiful creature, described as "elegant" by Tim Manolis.
We watched a group of Firetails ovipositing on an algal mass in a quiet area of the creek. 3-4 linked pairs were with a few inches of each other. The male didn't have to fly, as the female methodically flexed her abdomen down into the scum and pumped out her eggs, moving only occasionally. A video I took sort of shows the action, fwiw: http://www.flickr.com/photos/lenblumin/9625255522/
Taxonomy (I need this more than most of you!):
Order - Odonata - Dragonflies and Damselflies (over 5,000 species, with 450+ in North America)
Suborder - Zygoptera - The Damselflies - 22 families.
Family - Coenagrionidae - The Narrow-winged Damsels, or "Pond Damsels". This is a big family, with about 31 species in California alone. Included here are the Bluets, Dancers, Forktails and Firetails. The other main families seen here are the Broad-winged Damsels, Calopterygidae, where you'll find the Jewelwings and Rubyspots, and the Spread-winged Damsels, Lestidae.
Genus - Telebasis - The Firetails. Only 3 Firetail sp. are seen in the western U.S., and only one in California, but there are more than 50 other Firetail species found in the tropics. Most are red, but a few are blue.