diff --git a/django/db/models/lookups.py b/django/db/models/lookups.py
index 70cd525f30..d4edf2ce0f 100644
--- a/django/db/models/lookups.py
+++ b/django/db/models/lookups.py
@@ -508,21 +508,16 @@ class YearExact(YearLookup, Exact):
     lookup_name = 'exact'
 
     def as_sql(self, compiler, connection):
-        # We will need to skip the extract part and instead go
-        # directly with the originating field, that is self.lhs.lhs.
-        lhs_sql, params = self.process_lhs(compiler, connection, self.lhs.lhs)
-        rhs_sql, rhs_params = self.process_rhs(compiler, connection)
-        try:
-            # Check that rhs_params[0] exists (IndexError),
-            # it isn't None (TypeError), and is a number (ValueError)
-            int(rhs_params[0])
-        except (IndexError, TypeError, ValueError):
-            # Can't determine the bounds before executing the query, so skip
-            # optimizations by falling back to a standard exact comparison.
-            return super().as_sql(compiler, connection)
-        bounds = self.year_lookup_bounds(connection, rhs_params[0])
-        params.extend(bounds)
-        return '%s BETWEEN %%s AND %%s' % lhs_sql, params
+        # Avoid the extract operation if the rhs is a direct value to allow
+        # indexes to be used.
+        if self.rhs_is_direct_value():
+            # Skip the extract part by directly using the originating field,
+            # that is self.lhs.lhs.
+            lhs_sql, params = self.process_lhs(compiler, connection, self.lhs.lhs)
+            bounds = self.year_lookup_bounds(connection, self.rhs)
+            params.extend(bounds)
+            return '%s BETWEEN %%s AND %%s' % lhs_sql, params
+        return super().as_sql(compiler, connection)
 
 
 class YearGt(YearComparisonLookup):
diff --git a/tests/db_functions/datetime/test_extract_trunc.py b/tests/db_functions/datetime/test_extract_trunc.py
index 2088d09d06..f62bd0f0b2 100644
--- a/tests/db_functions/datetime/test_extract_trunc.py
+++ b/tests/db_functions/datetime/test_extract_trunc.py
@@ -4,7 +4,8 @@ import pytz
 
 from django.conf import settings
 from django.db.models import (
-    DateField, DateTimeField, IntegerField, Max, OuterRef, Subquery, TimeField,
+    DateField, DateTimeField, F, IntegerField, Max, OuterRef, Subquery,
+    TimeField,
 )
 from django.db.models.functions import (
     Extract, ExtractDay, ExtractHour, ExtractIsoYear, ExtractMinute,
@@ -108,6 +109,14 @@ class DateFunctionTests(TestCase):
                 query_string = str(qs.query).lower()
                 self.assertEqual(query_string.count(' between '), 1)
                 self.assertEqual(query_string.count('extract'), 0)
+                # an expression rhs cannot use the between optimization.
+                qs = DTModel.objects.annotate(
+                    start_year=ExtractYear('start_datetime'),
+                ).filter(end_datetime__year=F('start_year') + 1)
+                self.assertEqual(qs.count(), 1)
+                query_string = str(qs.query).lower()
+                self.assertEqual(query_string.count(' between '), 0)
+                self.assertEqual(query_string.count('extract'), 3)
 
     def test_extract_year_greaterthan_lookup(self):
         start_datetime = datetime(2015, 6, 15, 14, 10)