Well, after reading the suggestions I came up with a very similar way that works with 2.7.x without creating "funny" directory names (absolute-like names), and will only create the specified folder inside the zip.
Or just in case you needed your zip to contain a folder inside with the contents of the selected directory.
def zipDir( path, ziph ) :
"""
Inserts directory (path) into zipfile instance (ziph)
"""
for root, dirs, files in os.walk( path ) :
for file in files :
ziph.write( os.path.join( root, file ) , os.path.basename( os.path.normpath( path ) ) + "\\" + file )
def makeZip( pathToFolder ) :
"""
Creates a zip file with the specified folder
"""
zipf = zipfile.ZipFile( pathToFolder + 'file.zip', 'w', zipfile.ZIP_DEFLATED )
zipDir( pathToFolder, zipf )
zipf.close()
print( "Zip file saved to: " + pathToFolder)
makeZip( "c:\\path\\to\\folder\\to\\insert\\into\\zipfile" )