How can I make compilation more quiet by removing "LaTeX Warning" messages from the log?

How can I make compilation more quiet by removing "LaTeX Warning" messages
from the log?

I am using a the Tufte-\LaTeX class and compiling it in TextMate, which
has a nifty LaTeX bundle and latexmk interface. The document is getting
long, and I get heaps of these:
LaTeX Warning: Marginpar on page 31 moved.
This is mostly due to how the footnotes are handled by the class, and thus
rarely of interest to me. From time to time, I also get this from my
fonts:
LaTeX Font Warning: Font shape `OT1/zi4/m/it' undefined
As it happens, these issues are (really) trivial to me, but I do care
about the other issues that get lost in the huge list of warnings.
Is there a way to suppress either all or a selection of warnings from my
log? I could not find much on that topic by searching here or elsewhere.
(For the moment, it seems that my only option is to reprogram the TextMate
bundle to display warnings, e.g., in minuscule text.)