Should schools be able to strip-search students?

The recent Supreme Court ruling, that in 2003 an Arizona school violated the rights of one of it's students by strip-searching her while looking for contraband over-the-counter medication, spurred some interesting discussions at Child Caring and at Yahoo's Shine, where I wrote about it for their Parenting section. Here's the lede:

Remember what it was like to be 13? Awkward. Gawky. Embarrassed by your changing body. Worried about social pressure, fitting in, and being bullied by mean girls." Now imagine being strip searched in front of adults who are practically strangers. At school. ... [More]

The school's policy prohibits the use, possession or sale of any drug on school grounds, including prescription and over-the-counter medications. A week before the search, a student became sick after taking pills from a classmate and said certain students were bringing drugs to school. Which makes their reaction toward Redding and the possiblity that she had smuggled in some Advil a bit easier to understand, if not accept.

I understand the need to protect students, to ensure their health and safety, to eliminate the possiblity of drug abuse. But where do you draw the line?