Pandas Renaming MultiIndex values does not work at all (doesn't update values, or raise an exception)

Code Sample, a copy-pastable example if possible

df = pd.DataFrame({'First': ['A', 'A', 'A', 'B', 'B'], 'Last': ['C', 'D', 'E', 'E', 'F'], 'C':[1, 1, 2, 1, 1]})
df.set_index(['Last','First'], inplace=True)

# rename1
df.rename(index={('C','A'):('C','NEWFIRST')})

# rename2
df.rename(index={('C','A'):('NEWLAST','A')})

Problem description

Renaming Muiltiindex values does nothing, not even raise an Exception.

Expected Output

rename1 = pd.DataFrame({'First': ['NEWFIRST', 'A', 'A', 'B', 'B'], 'Last': ['C', 'D', 'E', 'E', 'F'], 'C':[1, 1, 2, 1, 1]})
rename1.set_index(['Last','First'], inplace=True)

rename2 = pd.DataFrame({'First': ['A', 'A', 'A', 'B', 'B'], 'Last': ['NEWLAST', 'D', 'E', 'E', 'F'], 'C':[1, 1, 2, 1, 1]})
rename2.set_index(['Last','First'], inplace=True)

Output of pd.show_versions()

INSTALLED VERSIONS
------------------
commit: None
python: 3.5.2.final.0
python-bits: 64
OS: Linux
OS-release: 4.8.0-46-generic
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: None
LANG: en_AU.UTF-8
LOCALE: en_AU.UTF-8

pandas: 0.19.2+0.g825876c.dirty
nose: 1.3.7
pip: 9.0.1
setuptools: 27.2.0
Cython: 0.25.2
numpy: 1.11.2
scipy: 0.18.1
statsmodels: 0.6.1
xarray: None
IPython: 5.1.0
sphinx: 1.5.1
patsy: 0.4.1
dateutil: 2.6.0
pytz: 2016.10
blosc: None
bottleneck: 1.1.0
tables: 3.3.0
numexpr: 2.6.1
matplotlib: 1.5.3
openpyxl: 2.4.0
xlrd: 1.0.0
xlwt: 1.1.2
xlsxwriter: 0.9.6
lxml: None
bs4: 4.5.1
html5lib: None
httplib2: None
apiclient: None
sqlalchemy: 1.1.4
pymysql: None
psycopg2: 2.6.2 (dt dec pq3 ext lo64)
jinja2: 2.8
boto: 2.45.0
pandas_datareader: None

Comment From: jorisvandenbossche

@gregsifr Thanks for the report. This is currently a known limitation of rename, see https://github.com/pandas-dev/pandas/issues/4160 (therefore closing this issue as a duplicate).

After https://github.com/pandas-dev/pandas/issues/13766 it will be possible to rename values in a specific level only, but that is of course not yet what is raised here.

Currenlty rename works by trying to rename individual labels of the different levels, hence the dict with tuples (as in your example) have no effect as they are not found. If we want to add this, we have to think about how the API could look like, or if there would be ambiguous cases if we try to infer that tuples are passed when having a MutliIndex.