diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 526b2c2e2c412..1a08609ccd99a 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3142,16 +3142,7 @@ def is_int(v):
         elif is_positional:
             indexer = key
         else:
-            try:
-                indexer = self.slice_indexer(start, stop, step, kind=kind)
-            except Exception:
-                if is_index_slice:
-                    if self.is_integer():
-                        raise
-                    else:
-                        indexer = key
-                else:
-                    raise
+            indexer = self.slice_indexer(start, stop, step, kind=kind)
 
         return indexer
 
@@ -4676,11 +4667,11 @@ def get_value(self, series, key):
                     raise InvalidIndexError(key)
                 else:
                     raise e1
-            except Exception:  # pragma: no cover
+            except Exception:
                 raise e1
         except TypeError:
-            # python 3
-            if is_scalar(key):  # pragma: no cover
+            # e.g. "[False] is an invalid key"
+            if is_scalar(key):
                 raise IndexError(key)
             raise InvalidIndexError(key)
 
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index 0fc74f4e78c9f..f085dff84462d 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -457,7 +457,11 @@ def __contains__(self, key):
             try:
                 self.get_loc(key)
                 return True
-            except Exception:
+            except (ValueError, TypeError, KeyError):
+                # TypeError can be reached if we pass a tuple that is not hashable
+                # ValueError can be reached if pass a 2-tuple and parse_time_string
+                #  raises with the wrong number of return values
+                #  TODO: the latter is a bug in parse_time_string
                 return False
 
     @cache_readonly
@@ -765,7 +769,9 @@ def _maybe_cast_slice_bound(self, label, side, kind):
                 _, parsed, reso = parse_time_string(label, self.freq)
                 bounds = self._parsed_string_to_bounds(reso, parsed)
                 return bounds[0 if side == "left" else 1]
-            except Exception:
+            except ValueError:
+                # string cannot be parsed as datetime-like
+                # TODO: we need tests for this case
                 raise KeyError(label)
         elif is_integer(label) or is_float(label):
             self._invalid_indexer("slice", label)
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index 755992c881fe5..62a74fefa6577 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -630,7 +630,8 @@ def insert(self, loc, item):
         if _is_convertible_to_td(item):
             try:
                 item = Timedelta(item)
-            except Exception:
+            except ValueError:
+                # e.g. str that can't be parsed to timedelta
                 pass
         elif is_scalar(item) and isna(item):
             # GH 18295