diff --git a/guide/src/class.md b/guide/src/class.md
index 1fd1009d488..9a2e48d4a70 100644
--- a/guide/src/class.md
+++ b/guide/src/class.md
@@ -271,7 +271,7 @@ You can also inherit native types such as `PyDict`, if they implement
 However, because of some technical problems, we don't currently provide safe upcasting methods for types
 that inherit native types. Even in such cases, you can unsafely get a base class by raw pointer conversion.
 
-```rust
+```rust,no_run
 # use pyo3::prelude::*;
 use pyo3::types::PyDict;
 use pyo3::{AsPyPointer, PyNativeType};
diff --git a/pyo3-derive-backend/src/from_pyobject.rs b/pyo3-derive-backend/src/from_pyobject.rs
index d4d097112ee..656532bea1e 100644
--- a/pyo3-derive-backend/src/from_pyobject.rs
+++ b/pyo3-derive-backend/src/from_pyobject.rs
@@ -249,7 +249,7 @@ impl<'a> Container<'a> {
         let self_ty = &self.path;
         let mut fields: Punctuated<TokenStream, syn::Token![,]> = Punctuated::new();
         for i in 0..len {
-            fields.push(quote!(slice[#i].extract()?));
+            fields.push(quote!(s.get_item(#i).extract()?));
         }
         let msg = if self.is_enum_variant {
             quote!(format!(
@@ -265,7 +265,6 @@ impl<'a> Container<'a> {
             if s.len() != #len {
                 return Err(::pyo3::exceptions::PyValueError::new_err(#msg))
             }
-            let slice = s.as_slice();
             Ok(#self_ty(#fields))
         )
     }
diff --git a/src/types/floatob.rs b/src/types/floatob.rs
index 0b0b5341310..5b773237069 100644
--- a/src/types/floatob.rs
+++ b/src/types/floatob.rs
@@ -83,7 +83,9 @@ impl<'source> FromPyObject<'source> for f32 {
 mod test {
     #[cfg(not(Py_LIMITED_API))]
     use crate::ffi::PyFloat_AS_DOUBLE;
-    use crate::{AsPyPointer, Python, ToPyObject};
+    #[cfg(not(Py_LIMITED_API))]
+    use crate::AsPyPointer;
+    use crate::{Python, ToPyObject};
 
     macro_rules! num_to_py_object_and_back (
         ($func_name:ident, $t1:ty, $t2:ty) => (
diff --git a/tests/test_buffer_protocol.rs b/tests/test_buffer_protocol.rs
index aca7ef1ca4e..c40e751b1e8 100644
--- a/tests/test_buffer_protocol.rs
+++ b/tests/test_buffer_protocol.rs
@@ -1,3 +1,5 @@
+#![cfg(not(Py_LIMITED_API))]
+
 use pyo3::buffer::PyBuffer;
 use pyo3::class::PyBufferProtocol;
 use pyo3::exceptions::PyBufferError;
diff --git a/tests/test_dunder.rs b/tests/test_dunder.rs
index 7b4ea91592d..e229e448181 100644
--- a/tests/test_dunder.rs
+++ b/tests/test_dunder.rs
@@ -457,6 +457,7 @@ fn test_cls_impl() {
 struct DunderDictSupport {}
 
 #[test]
+#[cfg_attr(Py_LIMITED_API, ignore)]
 fn dunder_dict_support() {
     let gil = Python::acquire_gil();
     let py = gil.python();
@@ -472,6 +473,7 @@ fn dunder_dict_support() {
 }
 
 #[test]
+#[cfg_attr(Py_LIMITED_API, ignore)]
 fn access_dunder_dict() {
     let gil = Python::acquire_gil();
     let py = gil.python();
@@ -493,6 +495,7 @@ struct InheritDict {
 }
 
 #[test]
+#[cfg_attr(Py_LIMITED_API, ignore)]
 fn inherited_dict() {
     let gil = Python::acquire_gil();
     let py = gil.python();
@@ -511,6 +514,7 @@ fn inherited_dict() {
 struct WeakRefDunderDictSupport {}
 
 #[test]
+#[cfg_attr(Py_LIMITED_API, ignore)]
 fn weakref_dunder_dict_support() {
     let gil = Python::acquire_gil();
     let py = gil.python();
diff --git a/tests/test_gc.rs b/tests/test_gc.rs
index b7aced4eecb..eb982887b93 100644
--- a/tests/test_gc.rs
+++ b/tests/test_gc.rs
@@ -150,6 +150,7 @@ fn gc_integration2() {
 struct WeakRefSupport {}
 
 #[test]
+#[cfg_attr(Py_LIMITED_API, ignore)]
 fn weakref_support() {
     let gil = Python::acquire_gil();
     let py = gil.python();
@@ -168,6 +169,7 @@ struct InheritWeakRef {
 }
 
 #[test]
+#[cfg_attr(Py_LIMITED_API, ignore)]
 fn inherited_weakref() {
     let gil = Python::acquire_gil();
     let py = gil.python();
@@ -269,6 +271,16 @@ impl PyGCProtocol for TraversableClass {
     }
 }
 
+#[cfg(PyPy)]
+unsafe fn get_type_traverse(tp: *mut pyo3::ffi::PyTypeObject) -> Option<pyo3::ffi::traverseproc> {
+    (*tp).tp_traverse
+}
+
+#[cfg(not(PyPy))]
+unsafe fn get_type_traverse(tp: *mut pyo3::ffi::PyTypeObject) -> Option<pyo3::ffi::traverseproc> {
+    std::mem::transmute(pyo3::ffi::PyType_GetSlot(tp, pyo3::ffi::Py_tp_traverse))
+}
+
 #[test]
 fn gc_during_borrow() {
     let gil = Python::acquire_gil();
@@ -285,7 +297,7 @@ fn gc_during_borrow() {
 
         // get the traverse function
         let ty = TraversableClass::type_object(py).as_type_ptr();
-        let traverse = (*ty).tp_traverse.unwrap();
+        let traverse = get_type_traverse(ty).unwrap();
 
         // create an object and check that traversing it works normally
         // when it's not borrowed
diff --git a/tests/test_inheritance.rs b/tests/test_inheritance.rs
index a2aad91a244..04fa732621f 100644
--- a/tests/test_inheritance.rs
+++ b/tests/test_inheritance.rs
@@ -168,7 +168,9 @@ impl SetWithName {
     }
 }
 
+// Subclassing builtin types is not allowed in the LIMITED API.
 #[test]
+#[cfg_attr(Py_LIMITED_API, should_panic)]
 fn inherit_set() {
     let gil = Python::acquire_gil();
     let py = gil.python();
@@ -195,7 +197,9 @@ impl DictWithName {
     }
 }
 
+// Subclassing builtin types is not allowed in the LIMITED API.
 #[test]
+#[cfg_attr(Py_LIMITED_API, should_panic)]
 fn inherit_dict() {
     let gil = Python::acquire_gil();
     let py = gil.python();
diff --git a/tests/test_pyfunction.rs b/tests/test_pyfunction.rs
index 89b4dbd01e3..f24f726682f 100644
--- a/tests/test_pyfunction.rs
+++ b/tests/test_pyfunction.rs
@@ -1,3 +1,4 @@
+#[cfg(not(Py_LIMITED_API))]
 use pyo3::buffer::PyBuffer;
 use pyo3::prelude::*;
 use pyo3::types::{PyCFunction, PyFunction};
@@ -23,6 +24,7 @@ fn test_optional_bool() {
     py_assert!(py, f, "f(None) == 'None'");
 }
 
+#[cfg(not(Py_LIMITED_API))]
 #[pyfunction]
 fn buffer_inplace_add(py: Python, x: PyBuffer<i32>, y: PyBuffer<i32>) {
     let x = x.as_mut_slice(py).unwrap();
@@ -33,6 +35,7 @@ fn buffer_inplace_add(py: Python, x: PyBuffer<i32>, y: PyBuffer<i32>) {
     }
 }
 
+#[cfg(not(Py_LIMITED_API))]
 #[test]
 fn test_buffer_add() {
     let gil = Python::acquire_gil();
diff --git a/tests/test_unsendable_dict.rs b/tests/test_unsendable_dict.rs
index 194b5888f83..86c974135d8 100644
--- a/tests/test_unsendable_dict.rs
+++ b/tests/test_unsendable_dict.rs
@@ -13,6 +13,7 @@ impl UnsendableDictClass {
 }
 
 #[test]
+#[cfg_attr(Py_LIMITED_API, ignore)]
 fn test_unsendable_dict() {
     let gil = Python::acquire_gil();
     let py = gil.python();
@@ -32,6 +33,7 @@ impl UnsendableDictClassWithWeakRef {
 }
 
 #[test]
+#[cfg_attr(Py_LIMITED_API, ignore)]
 fn test_unsendable_dict_with_weakref() {
     let gil = Python::acquire_gil();
     let py = gil.python();
diff --git a/tests/test_various.rs b/tests/test_various.rs
index 8a80df7d251..25c5e7bcb97 100644
--- a/tests/test_various.rs
+++ b/tests/test_various.rs
@@ -149,6 +149,7 @@ fn add_module(py: Python, module: &PyModule) -> PyResult<()> {
 }
 
 #[test]
+#[cfg_attr(Py_LIMITED_API, ignore)]
 fn test_pickle() {
     let gil = Python::acquire_gil();
     let py = gil.python();