Paul--
The distinction between annuals and perennials, of course, is whether the actual selfsame plant survives the winter. Many annuals will grow like, well, weeds if they are permitted to go to seed before they are tilled under (the seeds then get a nice dirt blanket for the winter) or simply allowed to go to seed; either way, they will grow healthy BIG time, as you say, the next season, especially where there has been a relatively mild winter. You may have created a Roundup-worthy monster, but at a minimum you might want to till under before it has a chance to reseed. Here's a <A target="_blank" HREF=http://www.fs.fed.us/database/feis/plants/graminoid/lolmul/value_and_use.html>websuite</A> with some additional information.