The above suggestion was first brought to my attention in this thread:
http://forum.musicasacra.com/forum/discussion/3518/advent-and-christmas/p1

Ad te levavi by Franz xaver Witt. Very simple harmony. It is also the correct text for the offertory on Advent Sunday I. If you need to lengthen it, chant some psalm verses from the 1935 Offertoriale.

Ad te levavi - Franz Xaver Witt (as suggested by hartleymartin) - Introit and Offertory of 1st Sunday of Advent

Conditor Alme Siderum – Michael Praetorius

Ecce concipies - Jacob Handl

Gaudete quia vobis - Charles Wood

Rorate Caeli - Christopher Tye (attached) - Introit of 4th Sunday of Advent

Some easier settings of Alma Redemptoris Mater, the proper Marian antiphon for Advent and Christmas. These are a bit longer, but well worth learning:
Juan Garcia de Salazar

Palestrina

Francesco Soriano

and Marian motets, some of which you can use at other times of the year
Dixit Maria - Hans Leo Hassler

Ave Maria – Cornelius Verdonck

Sicut Lilium Inter Spinas – Antoine Brumel - for Immaculate Conception

More ideas at Aristotle Esguerra's site.

Of all of these, I'd recommend Rorate Caeli (Tye), Dixit Maria (Hassler), and Ave Maria (Verdonck).

I sure hope not! My list is limited to the selections I'm familiar with, plus stuff I've happened to come across on cpdl - a very small batch considering all that's out there.

JS Batch or one of his sons?

Alma Redemptoris Mater by Palestrina
Veni, O Sapientia (Traditional)
Rorate Caeli by Leo Nestor
Veni, Jesu by Luigi Cherubini

PDQ Bach, Adam.

About the Hassler Dixit Maria, I have two different editions. Does anyone know whether the tenor's first B is a b-flat or b-natural? The editions I have differ on this point.

Personally, I think it's the most gratifying to sing the B-flat first, though that's not a scholarly opinion, just a musical one. : )

Charles,

I'm confused. How can both practices be "in keeping with period practice"?

I didn't say "both practices" ... the one note that gets the raised half degree is leading tone to a cadence, but the first B-flat plays no such role. Hassler even wrote out the raised cadencial half degree in the Soprano and Bass iterations of the same figure. In no case is the first B-flat of the figure raised to a B-natural. In two of three cases, the second B-flat is explicitly raised to B-natural in the original edition, and the one remaining case (in the Tenor part), one assumes either that Hassler overlooked raising the B-flat a half step, or it was a copyist error, or (most likely) Hassler intended to leave the B-flat alone, leaving it to performers to make a decision. It's important to note that the other two instances of the B-natural are pretty much required by the harmonic context of the other three parts (there is more ambiguity in the case of the Tenor part, because not all parts have entered the texture).

I'm attaching the appropriate pages from the partbooks of Hassler's Cantiones Sacrae for comparison (they are available at IMSLP). Incidentally, these show the correctness of the Ornes edition at CPDL.