Found my answer.
DoCmd.SetWarnings False
Here's a better one:
daoSQL = "DROP TABLE MyOldTable"
db.Execute daoSQL, dbFailOnError
It's better because you get a proper trappable error (if you don't have
permission to drop the table, or the table doesn't exist, and so on); and
because you can't forget to switch SetWarnings back on again.
By the way, if you are going to re-create the table again afterwards, it is
often easier and kinder to the mdb file to empty out the rows instead:
daoSQL = "DELETE FROM MyOldTable WHERE TRUE"
db.Execute daoSQL, dbFailOnError
All the best
Tim F