diff --git a/sphinx/application.py b/sphinx/application.py
index d6b781f59..168e48983 100644
--- a/sphinx/application.py
+++ b/sphinx/application.py
@@ -564,7 +564,7 @@ class Sphinx(object):
     def emit(self, event, *args):
         # type: (unicode, Any) -> List
         try:
-            logger.debug2('[app] emitting event: %r%s', event, repr(args)[:100])
+            logger.debug('[app] emitting event: %r%s', event, repr(args)[:100])
         except Exception:
             # not every object likes to be repr()'d (think
             # random stuff coming via autodoc)
diff --git a/sphinx/builders/__init__.py b/sphinx/builders/__init__.py
index 35bf52ad6..191646a94 100644
--- a/sphinx/builders/__init__.py
+++ b/sphinx/builders/__init__.py
@@ -391,7 +391,7 @@ class Builder(object):
                 self.write_doc(docname, doctree)
 
     def _write_parallel(self, docnames, nproc):
-        # type: (Iterable[unicode], int) -> None
+        # type: (Sequence[unicode], int) -> None
         def write_process(docs):
             # type: (List[Tuple[unicode, nodes.Node]]) -> None
             for docname, doctree in docs:
diff --git a/sphinx/builders/html.py b/sphinx/builders/html.py
index 2fd7a72a8..d9512b5df 100644
--- a/sphinx/builders/html.py
+++ b/sphinx/builders/html.py
@@ -732,7 +732,7 @@ class StandaloneHTMLBuilder(Builder):
                 reference.append(node)
 
     def load_indexer(self, docnames):
-        # type: (Set[unicode]) -> None
+        # type: (Iterable[unicode]) -> None
         keep = set(self.env.all_docs) - set(docnames)
         try:
             searchindexfn = path.join(self.outdir, self.searchindex_filename)
diff --git a/sphinx/domains/__init__.py b/sphinx/domains/__init__.py
index a90ee84aa..2389e342c 100644
--- a/sphinx/domains/__init__.py
+++ b/sphinx/domains/__init__.py
@@ -79,7 +79,7 @@ class Index(object):
         self.domain = domain
 
     def generate(self, docnames=None):
-        # type: (List[unicode]) -> Tuple[List[Tuple[unicode, List[List[Union[unicode, int]]]]], bool]  # NOQA
+        # type: (Iterable[unicode]) -> Tuple[List[Tuple[unicode, List[List[Union[unicode, int]]]]], bool]  # NOQA
         """Return entries for the index given by *name*.  If *docnames* is
         given, restrict to entries referring to these docnames.
 
@@ -107,7 +107,7 @@ class Index(object):
 
         Qualifier and description are not rendered e.g. in LaTeX output.
         """
-        return []
+        return tuple()
 
 
 class Domain(object):
diff --git a/sphinx/domains/python.py b/sphinx/domains/python.py
index 886b1f863..2efc6db0b 100644
--- a/sphinx/domains/python.py
+++ b/sphinx/domains/python.py
@@ -27,7 +27,7 @@ from sphinx.util.docfields import Field, GroupedField, TypedField
 
 if False:
     # For type annotation
-    from typing import Any, Iterator, Tuple, Union  # NOQA
+    from typing import Any, Iterable, Iterator, Tuple, Union  # NOQA
     from sphinx.application import Sphinx  # NOQA
     from sphinx.builders import Builder  # NOQA
     from sphinx.environment import BuildEnvironment  # NOQA
@@ -582,7 +582,7 @@ class PythonModuleIndex(Index):
     shortname = l_('modules')
 
     def generate(self, docnames=None):
-        # type: (List[unicode]) -> Tuple[List[Tuple[unicode, List[List[Union[unicode, int]]]]], bool]  # NOQA
+        # type: (Iterable[unicode]) -> Tuple[List[Tuple[unicode, List[List[Union[unicode, int]]]]], bool]  # NOQA
         content = {}  # type: Dict[unicode, List]
         # list of prefixes to ignore
         ignores = None  # type: List[unicode]
diff --git a/sphinx/ext/intersphinx.py b/sphinx/ext/intersphinx.py
index cc321e386..af39722ce 100644
--- a/sphinx/ext/intersphinx.py
+++ b/sphinx/ext/intersphinx.py
@@ -272,7 +272,7 @@ def load_mappings(app):
 
         if isinstance(value, (list, tuple)):
             # new format
-            name, (uri, inv) = key, value
+            name, (uri, inv) = key, value  # type: ignore
             if not isinstance(name, string_types):
                 logger.warning('intersphinx identifier %r is not string. Ignored', name)
                 continue
diff --git a/sphinx/util/parallel.py b/sphinx/util/parallel.py
index 9246841e5..1d97a511c 100644
--- a/sphinx/util/parallel.py
+++ b/sphinx/util/parallel.py
@@ -88,7 +88,7 @@ class ParallelTasks(object):
             failed = False
         except BaseException as err:
             failed = True
-            errmsg = traceback.format_exception_only(err.__class__, err)[0].strip()
+            errmsg = traceback.format_exception_only(err.__class__, err)[0].strip()  # type: ignore  # NOQA
             ret = (errmsg, traceback.format_exc())
         logging.convert_serializable(collector.logs)
         pipe.send((failed, collector.logs, ret))
diff --git a/sphinx/util/requests.py b/sphinx/util/requests.py
index 3f6ff3879..03e815c2c 100644
--- a/sphinx/util/requests.py
+++ b/sphinx/util/requests.py
@@ -22,7 +22,7 @@ try:
 except ImportError:
     # python-requests package in Debian jessie does not provide ``requests.packages.urllib3``.
     # So try to import the exceptions from urllib3 package.
-    from urllib3.exceptions import SSLError, InsecureRequestWarning
+    from urllib3.exceptions import SSLError, InsecureRequestWarning  # type: ignore
 
 # try to load requests[security]
 try: