diff --git a/pandas/core/arrays/interval.py b/pandas/core/arrays/interval.py
index b11736248c12a..f5167f470b056 100644
--- a/pandas/core/arrays/interval.py
+++ b/pandas/core/arrays/interval.py
@@ -725,45 +725,18 @@ def _concat_same_type(cls, to_concat):
         right = np.concatenate([interval.right for interval in to_concat])
         return cls._simple_new(left, right, closed=closed, copy=False)
 
-    def _shallow_copy(self, left=None, right=None, closed=None):
+    def _shallow_copy(self, left, right):
         """
         Return a new IntervalArray with the replacement attributes
 
         Parameters
         ----------
-        left : array-like
+        left : Index
             Values to be used for the left-side of the intervals.
-            If None, the existing left and right values will be used.
-
-        right : array-like
+        right : Index
             Values to be used for the right-side of the intervals.
-            If None and left is IntervalArray-like, the left and right
-            of the IntervalArray-like will be used.
-
-        closed : {'left', 'right', 'both', 'neither'}, optional
-            Whether the intervals are closed on the left-side, right-side, both
-            or neither.  If None, the existing closed will be used.
         """
-        if left is None:
-
-            # no values passed
-            left, right = self.left, self.right
-
-        elif right is None:
-
-            # only single value passed, could be an IntervalArray
-            # or array of Intervals
-            if not isinstance(left, (type(self), ABCIntervalIndex)):
-                left = type(self)(left)
-
-            left, right = left.left, left.right
-        else:
-
-            # both left and right are values
-            pass
-
-        closed = closed or self.closed
-        return self._simple_new(left, right, closed=closed, verify_integrity=False)
+        return self._simple_new(left, right, closed=self.closed, verify_integrity=False)
 
     def copy(self):
         """
@@ -1035,7 +1008,9 @@ def set_closed(self, closed):
             msg = f"invalid option for 'closed': {closed}"
             raise ValueError(msg)
 
-        return self._shallow_copy(closed=closed)
+        return type(self)._simple_new(
+            left=self.left, right=self.right, closed=closed, verify_integrity=False
+        )
 
     @property
     def length(self):
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 6ea4250e4acf4..b3923a1298859 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -333,11 +333,12 @@ def from_tuples(
     # --------------------------------------------------------------------
 
     @Appender(Index._shallow_copy.__doc__)
-    def _shallow_copy(self, left=None, right=None, **kwargs):
-        result = self._data._shallow_copy(left=left, right=right)
+    def _shallow_copy(self, values=None, **kwargs):
+        if values is None:
+            values = self._data
         attributes = self._get_attributes_dict()
         attributes.update(kwargs)
-        return self._simple_new(result, **attributes)
+        return self._simple_new(values, **attributes)
 
     @cache_readonly
     def _isnan(self):
@@ -407,7 +408,7 @@ def astype(self, dtype, copy=True):
         with rewrite_exception("IntervalArray", type(self).__name__):
             new_values = self.values.astype(dtype, copy=copy)
         if is_interval_dtype(new_values):
-            return self._shallow_copy(new_values.left, new_values.right)
+            return self._shallow_copy(new_values)
         return Index.astype(self, dtype, copy=copy)
 
     @property
@@ -881,7 +882,8 @@ def where(self, cond, other=None):
         if other is None:
             other = self._na_value
         values = np.where(cond, self.values, other)
-        return self._shallow_copy(values)
+        result = IntervalArray(values)
+        return self._shallow_copy(result)
 
     def delete(self, loc):
         """
@@ -893,7 +895,8 @@ def delete(self, loc):
         """
         new_left = self.left.delete(loc)
         new_right = self.right.delete(loc)
-        return self._shallow_copy(new_left, new_right)
+        result = self._data._shallow_copy(new_left, new_right)
+        return self._shallow_copy(result)
 
     def insert(self, loc, item):
         """
@@ -927,7 +930,8 @@ def insert(self, loc, item):
 
         new_left = self.left.insert(loc, left_insert)
         new_right = self.right.insert(loc, right_insert)
-        return self._shallow_copy(new_left, new_right)
+        result = self._data._shallow_copy(new_left, new_right)
+        return self._shallow_copy(result)
 
     @Appender(_index_shared_docs["take"] % _index_doc_kwargs)
     def take(self, indices, axis=0, allow_fill=True, fill_value=None, **kwargs):