diff --git a/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/eq.md b/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/eq.md
index f9de673a17..cb61ecf5f6 100644
--- a/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/eq.md
+++ b/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/eq.md
@@ -12,6 +12,30 @@ def _(flag: bool):
         reveal_type(x)  # revealed: None
 ```
 
+## `None != x` (reversed operands)
+
+```py
+def _(flag: bool):
+    x = None if flag else 1
+
+    if None != x:
+        reveal_type(x)  # revealed: Literal[1]
+    else:
+        reveal_type(x)  # revealed: None
+```
+
+This also works for `==` with reversed operands:
+
+```py
+def _(flag: bool):
+    x = None if flag else 1
+
+    if None == x:
+        reveal_type(x)  # revealed: None
+    else:
+        reveal_type(x)  # revealed: Literal[1]
+```
+
 ## `!=` for other singleton types
 
 ### Bool
diff --git a/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/in.md b/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/in.md
index 79bb4c1d92..660ef375e7 100644
--- a/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/in.md
+++ b/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/in.md
@@ -121,6 +121,31 @@ def test(x: Literal["a", "b", "c"] | None | int = None):
         reveal_type(x)  # revealed: Literal["a", "c"] | int
 ```
 
+## No narrowing for the right-hand side (currently)
+
+No narrowing is done for the right-hand side currently, even if the right-hand side is a valid
+"target" (name/attribute/subscript) that could potentially be narrowed. We may change this in the
+future:
+
+```py
+from typing import Literal
+
+def f(x: Literal["abc", "def"]):
+    if "a" in x:
+        # `x` could also be validly narrowed to `Literal["abc"]` here:
+        reveal_type(x)  # revealed: Literal["abc", "def"]
+    else:
+        # `x` could also be validly narrowed to `Literal["def"]` here:
+        reveal_type(x)  # revealed: Literal["abc", "def"]
+
+    if "a" not in x:
+        # `x` could also be validly narrowed to `Literal["def"]` here:
+        reveal_type(x)  # revealed: Literal["abc", "def"]
+    else:
+        # `x` could also be validly narrowed to `Literal["abc"]` here:
+        reveal_type(x)  # revealed: Literal["abc", "def"]
+```
+
 ## bool
 
 ```py
diff --git a/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/is_not.md b/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/is_not.md
index 0c4e87c36c..c85e42fc6f 100644
--- a/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/is_not.md
+++ b/crates/ty_python_semantic/resources/mdtest/narrow/conditionals/is_not.md
@@ -16,6 +16,32 @@ def _(flag: bool):
     reveal_type(x)  # revealed: None | Literal[1]
 ```
 
+## `None is not x` (reversed operands)
+
+```py
+def _(flag: bool):
+    x = None if flag else 1
+
+    if None is not x:
+        reveal_type(x)  # revealed: Literal[1]
+    else:
+        reveal_type(x)  # revealed: None
+
+    reveal_type(x)  # revealed: None | Literal[1]
+```
+
+This also works for other singleton types with reversed operands:
+
+```py
+def _(flag: bool):
+    x = True if flag else False
+
+    if False is not x:
+        reveal_type(x)  # revealed: Literal[True]
+    else:
+        reveal_type(x)  # revealed: Literal[False]
+```
+
 ## `is not` for other singleton types
 
 Boolean literals:
diff --git a/crates/ty_python_semantic/src/types/narrow.rs b/crates/ty_python_semantic/src/types/narrow.rs
index 49461f9d06..435a1c6b64 100644
--- a/crates/ty_python_semantic/src/types/narrow.rs
+++ b/crates/ty_python_semantic/src/types/narrow.rs
@@ -1250,6 +1250,29 @@ impl<'db, 'ast> NarrowingConstraintsBuilder<'db, 'ast> {
                         );
                     }
                 }
+                // For symmetric operators (==, !=, is, is not), if left is not a narrowable target,
+                // try to narrow the right operand instead by swapping the operands.
+                // E.g., `None != x` should narrow `x` the same way as `x != None`.
+                _ if matches!(
+                    op,
+                    ast::CmpOp::Eq | ast::CmpOp::NotEq | ast::CmpOp::Is | ast::CmpOp::IsNot
+                ) && matches!(
+                    right,
+                    ast::Expr::Name(_)
+                        | ast::Expr::Attribute(_)
+                        | ast::Expr::Subscript(_)
+                        | ast::Expr::Named(_)
+                ) =>
+                {
+                    if let Some(right_place) = place_expr(right)
+                        // Swap lhs_ty and rhs_ty since we're narrowing the right operand
+                        && let Some(ty) =
+                            self.evaluate_expr_compare_op(rhs_ty, lhs_ty, *op, is_positive)
+                    {
+                        let place = self.expect_place(&right_place);
+                        constraints.insert(place, NarrowingConstraint::regular(ty));
+                    }
+                }
                 _ => {}
             }
         }