diff --git a/crates/red_knot_python_semantic/resources/mdtest/type_properties/is_equivalent_to.md b/crates/red_knot_python_semantic/resources/mdtest/type_properties/is_equivalent_to.md
index 8ae96d733aaba5..44fa07756c2bcd 100644
--- a/crates/red_knot_python_semantic/resources/mdtest/type_properties/is_equivalent_to.md
+++ b/crates/red_knot_python_semantic/resources/mdtest/type_properties/is_equivalent_to.md
@@ -84,4 +84,26 @@ static_assert(
 )
 ```
 
+## Unions containing tuples containing tuples containing unions (etc.)
+
+```py
+from knot_extensions import is_equivalent_to, static_assert, Intersection
+
+class P: ...
+class Q: ...
+
+static_assert(
+    is_equivalent_to(
+        tuple[tuple[tuple[P | Q]]] | P,
+        tuple[tuple[tuple[Q | P]]] | P,
+    )
+)
+static_assert(
+    is_equivalent_to(
+        tuple[tuple[tuple[tuple[tuple[Intersection[P, Q]]]]]],
+        tuple[tuple[tuple[tuple[tuple[Intersection[Q, P]]]]]],
+    )
+)
+```
+
 [the equivalence relation]: https://typing.readthedocs.io/en/latest/spec/glossary.html#term-equivalent
diff --git a/crates/red_knot_python_semantic/src/types.rs b/crates/red_knot_python_semantic/src/types.rs
index 69940e4a9d78f9..14dfb013946c0e 100644
--- a/crates/red_knot_python_semantic/src/types.rs
+++ b/crates/red_knot_python_semantic/src/types.rs
@@ -811,6 +811,35 @@ impl<'db> Type<'db> {
         }
     }
 
+    /// Return a normalized version of `self` in which all unions and intersections are sorted
+    /// according to a canonical order, no matter how "deeply" a union/intersection may be nested.
+    #[must_use]
+    pub fn with_sorted_unions(self, db: &'db dyn Db) -> Self {
+        match self {
+            Type::Union(union) => Type::Union(union.to_sorted_union(db)),
+            Type::Intersection(intersection) => {
+                Type::Intersection(intersection.to_sorted_intersection(db))
+            }
+            Type::Tuple(tuple) => Type::Tuple(tuple.with_sorted_unions(db)),
+            Type::LiteralString
+            | Type::Instance(_)
+            | Type::AlwaysFalsy
+            | Type::AlwaysTruthy
+            | Type::BooleanLiteral(_)
+            | Type::SliceLiteral(_)
+            | Type::BytesLiteral(_)
+            | Type::StringLiteral(_)
+            | Type::Dynamic(_)
+            | Type::Never
+            | Type::FunctionLiteral(_)
+            | Type::ModuleLiteral(_)
+            | Type::ClassLiteral(_)
+            | Type::KnownInstance(_)
+            | Type::IntLiteral(_)
+            | Type::SubclassOf(_) => self,
+        }
+    }
+
     /// Return true if this type is a [subtype of] type `target`.
     ///
     /// This method returns `false` if either `self` or `other` is not fully static.
@@ -1154,7 +1183,7 @@ impl<'db> Type<'db> {
                 left.is_equivalent_to(db, right)
             }
             (Type::Tuple(left), Type::Tuple(right)) => left.is_equivalent_to(db, right),
-            _ => self.is_fully_static(db) && other.is_fully_static(db) && self == other,
+            _ => self == other && self.is_fully_static(db) && other.is_fully_static(db),
         }
     }
 
@@ -4352,12 +4381,11 @@ impl<'db> UnionType<'db> {
     /// Create a new union type with the elements sorted according to a canonical ordering.
     #[must_use]
     pub fn to_sorted_union(self, db: &'db dyn Db) -> Self {
-        let mut new_elements = self.elements(db).to_vec();
-        for element in &mut new_elements {
-            if let Type::Intersection(intersection) = element {
-                intersection.sort(db);
-            }
-        }
+        let mut new_elements: Vec<Type<'db>> = self
+            .elements(db)
+            .iter()
+            .map(|element| element.with_sorted_unions(db))
+            .collect();
         new_elements.sort_unstable_by(union_elements_ordering);
         UnionType::new(db, new_elements.into_boxed_slice())
     }
@@ -4453,19 +4481,24 @@ impl<'db> IntersectionType<'db> {
     /// according to a canonical ordering.
     #[must_use]
     pub fn to_sorted_intersection(self, db: &'db dyn Db) -> Self {
-        let mut positive = self.positive(db).clone();
-        positive.sort_unstable_by(union_elements_ordering);
-
-        let mut negative = self.negative(db).clone();
-        negative.sort_unstable_by(union_elements_ordering);
+        fn normalized_set<'db>(
+            db: &'db dyn Db,
+            elements: &FxOrderSet<Type<'db>>,
+        ) -> FxOrderSet<Type<'db>> {
+            let mut elements: FxOrderSet<Type<'db>> = elements
+                .iter()
+                .map(|ty| ty.with_sorted_unions(db))
+                .collect();
 
-        IntersectionType::new(db, positive, negative)
-    }
+            elements.sort_unstable_by(union_elements_ordering);
+            elements
+        }
 
-    /// Perform an in-place sort of this [`IntersectionType`] instance
-    /// according to a canonical ordering.
-    fn sort(&mut self, db: &'db dyn Db) {
-        *self = self.to_sorted_intersection(db);
+        IntersectionType::new(
+            db,
+            normalized_set(db, self.positive(db)),
+            normalized_set(db, self.negative(db)),
+        )
     }
 
     pub fn is_fully_static(self, db: &'db dyn Db) -> bool {
@@ -4608,6 +4641,18 @@ impl<'db> TupleType<'db> {
         Type::Tuple(Self::new(db, elements.into_boxed_slice()))
     }
 
+    /// Return a normalized version of `self` in which all unions and intersections are sorted
+    /// according to a canonical order, no matter how "deeply" a union/intersection may be nested.
+    #[must_use]
+    pub fn with_sorted_unions(self, db: &'db dyn Db) -> Self {
+        let elements: Box<[Type<'db>]> = self
+            .elements(db)
+            .iter()
+            .map(|ty| ty.with_sorted_unions(db))
+            .collect();
+        TupleType::new(db, elements)
+    }
+
     pub fn is_equivalent_to(self, db: &'db dyn Db, other: Self) -> bool {
         let self_elements = self.elements(db);
         let other_elements = other.elements(db);