You could help speed up decomposition by covering a green manure. The Interbay Mulch technique works well, see 'Interbay Mulch' on the Soil FAQ Page here.

SARE has good information on green manures. They publish a 248 page book, Managing Cover Crops Profitably, which is available free online as a PDF file.

All the best,
-Patrick

Here is a link that might be useful: Managing Cover Crops Profitably

I've not ever deliberatly planted annual ryegrass even for a cover crop, Field, Winter, or Cereal Rye is what I use and lately in the spring all I do is cover that with newspaper and some shredded leaves rather than tilling it into the soil. As a rule, because of how they are constructed, Lasagna beds usually do not have cover crops grown on them, and no till, because they are usually covered with a heavy mulch, are usually not planted in cover crops because if that mulch. Both types of beds usually have more than ample quantities of organic matter and do not need a green manure or cover crop, too and that is why there is little information about tilling in green manure, cover crops, into one of those.

kimmsr, I'm sorry, I planted cereal rye, not ryegrass. We have a mild climate in my lower part of zone 7 and I wanted to add to my beds this winter. I wanted to increase the abundance of mycorrhizal spores in my lasagna beds. Also, since I am using oak leaves for my brown, I have a ridiculous amount of oak sprouts every spring and they are tenacious. I was hoping the weed-suppressing allelopathic compounds in the rye and the smothering cover of the rye would help defeat the mighty acorns. Sorry about the confusion.
Madmagic, thank you for the cover crop pdf. I haven't read it cover to cover, ahem, but it has some fascinating info within. Interbay mulch, yes, I'm following most of the same principles, but burlap is not in the budget. Given time I can certainly scrouge some. But for now I will follow as kimmsr leads, and use newspaper covered with shredded leaves over my decaying cereal rye.
Thank you so much for your clarifications.

You're welcome, Dizzyjane. :) SARE has shorter overviews on cover crops, though I have found lots of useful info scattered throughout the book linked. And they do have a good section on rye.

Regarding burlap, don't think it's always required for the Interbay process. A year ago last fall I covered up a lasagna heap with paper from torn-up yard waste bags, and it worked just fine -- rainwater and snowmelt easily soaked through, yet it kept off the birds and other predators quite well. In the spring, everything in the lasagna pile except the thicker sticks and twigs had broken down into beautiful compost. Plants did especially well in that section of the garden over the growing season, and it wasn't tilled.

Newspaper, perhaps even cardboard, should also work well as Kimmsr suggested. Perhaps even help keep the acorns from sprouting?

All the best,
-Patrick

I just lay down some newspaper over the Field, Winter, Cereal Rye planted in my Aspargus bed and that takes care of it. Burlap is always used to cover the Interbay Mulch (actually a composting process) according to Jon Rowley, but you need to look at the burlap and determine if what you have is real burlap or is made from a synthetic fiber. Real burlap is still made from Jute, a natural fiber that will eventually be digested by the soil bacteria while much "burlap" today is being made from some plastic fiber.

I got newspaper down yesterday before Ma Nature put 3 inches of snow on top!
Thanks y'all!