Atrichum undulatum is what i had always called this plant. This is what is was in Crum's Mosses of Eastern North America. He had split it into several varieties: var altecristatum, var undulatum, var attenuatum, and var oerstedianum. i never bothered with these and just called the plant Atrichum undulatum. When i got my new copy of Flora of North America, i looked further into this species. It said: "No Atrichum species occurring in North America has been as widely misunderstood as A. undulatum....Its occurrence in North America has not been demonstrated. As used by American authors, it probably refers to A. altecristatum." Atrichum crispulum had also been recently called Atrichum oerstedianum, but comparisons to the type specimen indicate that the two are separate with A. oerstedianum being found in Mexico and Central America.
So, ok, we don't have A. undulatum, what we DO have is A. crispulum and A. altecristatum from that complex. In working on my wooded wetlands project, i've come across several specimens and this is how to tell the two species apart...since i didn't have the exact substrate for the specimen (Apparently A. altecristatum prefers soil banks, along roads & trails, on hummocks - more like A. angustatum and A. crispulum prefers soil in mostly shaded habitats, often wet banks along streams or at the margins of fens or swamps), i had to make leaf cross sections to look at the height of the lamellae (which are the long ridges that are lined up along the costa). Almost all the specimens i looked at were A crispulum...it has 4-6 lamellae that are very short, usually they were 3 cells high. In A. altecristatum, the lamellae are 4-6 cells high. If you're lucky enough to collect a fruiting plant, A. crispulum has a capsule that is curved and inclined (see the photos and drawings below), whereas A. altecristatum capsule is usually more straight and erect.