diff --git a/sqlglot/optimizer/simplify.py b/sqlglot/optimizer/simplify.py
index 6dfd9ff6eb..06ea423bb9 100644
--- a/sqlglot/optimizer/simplify.py
+++ b/sqlglot/optimizer/simplify.py
@@ -495,6 +495,17 @@ def simplify_coalesce(expression):
     )
 
 
+# CROSS joins result in an empty table if the right table is empty.
+# So we can only simplify certain types of joins to CROSS.
+# Or in other words, LEFT JOIN x ON TRUE != CROSS JOIN x
+JOINS = {
+    ("", ""),
+    ("", "INNER"),
+    ("RIGHT", ""),
+    ("RIGHT", "OUTER"),
+}
+
+
 def remove_where_true(expression):
     for where in expression.find_all(exp.Where):
         if always_true(where.this):
@@ -504,6 +515,7 @@ def remove_where_true(expression):
             always_true(join.args.get("on"))
             and not join.args.get("using")
             and not join.args.get("method")
+            and (join.side, join.kind) in JOINS
         ):
             join.set("on", None)
             join.set("side", None)
diff --git a/tests/fixtures/optimizer/simplify.sql b/tests/fixtures/optimizer/simplify.sql
index ff42baca1b..629262dcf4 100644
--- a/tests/fixtures/optimizer/simplify.sql
+++ b/tests/fixtures/optimizer/simplify.sql
@@ -240,9 +240,18 @@ A AND B AND C;
 SELECT x WHERE TRUE;
 SELECT x;
 
-SELECT x FROM y LEFT JOIN z ON TRUE;
+SELECT x FROM y JOIN z ON TRUE;
+SELECT x FROM y CROSS JOIN z;
+
+SELECT x FROM y RIGHT JOIN z ON TRUE;
 SELECT x FROM y CROSS JOIN z;
 
+SELECT x FROM y LEFT JOIN z ON TRUE;
+SELECT x FROM y LEFT JOIN z ON TRUE;
+
+SELECT x FROM y FULL OUTER JOIN z ON TRUE;
+SELECT x FROM y FULL OUTER JOIN z ON TRUE;
+
 SELECT x FROM y JOIN z USING (x);
 SELECT x FROM y JOIN z USING (x);