diff --git a/django/db/models/expressions.py b/django/db/models/expressions.py
index 5b5a0ae4aa..a9768919a2 100644
--- a/django/db/models/expressions.py
+++ b/django/db/models/expressions.py
@@ -1145,11 +1145,9 @@ class Exists(Subquery):
     output_field = fields.BooleanField()
 
     def __init__(self, queryset, negated=False, **kwargs):
-        # As a performance optimization, remove ordering since EXISTS doesn't
-        # care about it, just whether or not a row matches.
-        queryset = queryset.order_by()
         self.negated = negated
         super().__init__(queryset, **kwargs)
+        self.query = self.query.exists()
 
     def __invert__(self):
         clone = self.copy()
diff --git a/django/db/models/sql/compiler.py b/django/db/models/sql/compiler.py
index fc7a7aafae..b321762303 100644
--- a/django/db/models/sql/compiler.py
+++ b/django/db/models/sql/compiler.py
@@ -1127,9 +1127,6 @@ class SQLCompiler:
         Backends (e.g. NoSQL) can override this in order to use optimized
         versions of "query has any results."
         """
-        # This is always executed on a query clone, so we can modify self.query
-        self.query.add_extra({'a': 1}, None, None, None, None, None)
-        self.query.set_extra_mask(['a'])
         return bool(self.execute_sql(SINGLE))
 
     def execute_sql(self, result_type=MULTI, chunked_fetch=False, chunk_size=GET_ITERATOR_CHUNK_SIZE):
diff --git a/django/db/models/sql/query.py b/django/db/models/sql/query.py
index 659fa87314..4648daf395 100644
--- a/django/db/models/sql/query.py
+++ b/django/db/models/sql/query.py
@@ -522,7 +522,7 @@ class Query(BaseExpression):
     def has_filters(self):
         return self.where
 
-    def has_results(self, using):
+    def exists(self):
         q = self.clone()
         if not q.distinct:
             if q.group_by is True:
@@ -533,6 +533,12 @@ class Query(BaseExpression):
             q.clear_select_clause()
         q.clear_ordering(True)
         q.set_limits(high=1)
+        q.add_extra({'a': 1}, None, None, None, None, None)
+        q.set_extra_mask(['a'])
+        return q
+
+    def has_results(self, using):
+        q = self.exists()
         compiler = q.get_compiler(using=using)
         return compiler.has_results()
 
diff --git a/tests/expressions/tests.py b/tests/expressions/tests.py
index 2f392a51e6..c15204ce33 100644
--- a/tests/expressions/tests.py
+++ b/tests/expressions/tests.py
@@ -22,7 +22,7 @@ from django.db.models.functions import (
 from django.db.models.sql import constants
 from django.db.models.sql.datastructures import Join
 from django.test import SimpleTestCase, TestCase, skipUnlessDBFeature
-from django.test.utils import Approximate, isolate_apps
+from django.test.utils import Approximate, CaptureQueriesContext, isolate_apps
 from django.utils.functional import SimpleLazyObject
 
 from .models import (
@@ -1738,6 +1738,26 @@ class ValueTests(TestCase):
             Value(object()).output_field
 
 
+class ExistsTests(TestCase):
+    def test_optimizations(self):
+        with CaptureQueriesContext(connection) as context:
+            list(Experiment.objects.values(exists=Exists(
+                Experiment.objects.order_by('pk'),
+            )).order_by())
+        captured_queries = context.captured_queries
+        self.assertEqual(len(captured_queries), 1)
+        captured_sql = captured_queries[0]['sql']
+        self.assertNotIn(
+            connection.ops.quote_name(Experiment._meta.pk.column),
+            captured_sql,
+        )
+        self.assertIn(
+            connection.ops.limit_offset_sql(None, 1),
+            captured_sql,
+        )
+        self.assertNotIn('ORDER BY', captured_sql)
+
+
 class FieldTransformTests(TestCase):
 
     @classmethod