diff --git a/src/greenlet/TPythonState.cpp b/src/greenlet/TPythonState.cpp
index 465d4174..c0dbf703 100644
--- a/src/greenlet/TPythonState.cpp
+++ b/src/greenlet/TPythonState.cpp
@@ -130,11 +130,13 @@ void PythonState::operator<<(const PyThreadState *const tstate) noexcept
 #if GREENLET_PY311
   #if GREENLET_PY312
     this->py_recursion_depth = tstate->py_recursion_limit - tstate->py_recursion_remaining;
-    this->c_recursion_depth = C_RECURSION_LIMIT - tstate->c_recursion_remaining;
+    this->c_recursion_depth = Py_C_RECURSION_LIMIT - tstate->c_recursion_remaining;
   #else // not 312
     this->recursion_depth = tstate->recursion_limit - tstate->recursion_remaining;
   #endif // GREENLET_PY312
+  #if GREENLET_USE_CFRAME
     this->current_frame = tstate->cframe->current_frame;
+  #endif
     this->datastack_chunk = tstate->datastack_chunk;
     this->datastack_top = tstate->datastack_top;
     this->datastack_limit = tstate->datastack_limit;
@@ -199,12 +201,14 @@ void PythonState::operator>>(PyThreadState *const tstate) noexcept
 #if GREENLET_PY311
   #if GREENLET_PY312
     tstate->py_recursion_remaining = tstate->py_recursion_limit - this->py_recursion_depth;
-    tstate->c_recursion_remaining = C_RECURSION_LIMIT - this->c_recursion_depth;
+    tstate->c_recursion_remaining = Py_C_RECURSION_LIMIT - this->c_recursion_depth;
     this->unexpose_frames();
   #else // \/ 3.11
     tstate->recursion_remaining = tstate->recursion_limit - this->recursion_depth;
   #endif // GREENLET_PY312
+  #if GREENLET_USE_CFRAME
     tstate->cframe->current_frame = this->current_frame;
+  #endif
     tstate->datastack_chunk = this->datastack_chunk;
     tstate->datastack_top = this->datastack_top;
     tstate->datastack_limit = this->datastack_limit;
@@ -238,7 +242,7 @@ void PythonState::set_initial_state(const PyThreadState* const tstate) noexcept
 #if GREENLET_PY312
     this->py_recursion_depth = tstate->py_recursion_limit - tstate->py_recursion_remaining;
     // XXX: TODO: Comment from a reviewer:
-    //     Should this be ``C_RECURSION_LIMIT - tstate->c_recursion_remaining``?
+    //     Should this be ``Py_C_RECURSION_LIMIT - tstate->c_recursion_remaining``?
     // But to me it looks more like that might not be the right
     // initialization either?
     this->c_recursion_depth = tstate->py_recursion_limit - tstate->py_recursion_remaining;
diff --git a/src/greenlet/greenlet_cpython_compat.hpp b/src/greenlet/greenlet_cpython_compat.hpp
index cdc1617f..c0fb94c5 100644
--- a/src/greenlet/greenlet_cpython_compat.hpp
+++ b/src/greenlet/greenlet_cpython_compat.hpp
@@ -12,19 +12,24 @@
 
 #if PY_VERSION_HEX >= 0x30A00B1
 #    define GREENLET_PY310 1
+#else
+#    define GREENLET_PY310 0
+#endif
+
 /*
 Python 3.10 beta 1 changed tstate->use_tracing to a nested cframe member.
 See https://github.com/python/cpython/pull/25276
 We have to save and restore this as well.
+
+Python 3.13 removed PyThreadState.cframe (GH-108035).
 */
+#if GREENLET_PY310 && PY_VERSION_HEX < 0x30D0000
 #    define GREENLET_USE_CFRAME 1
 #else
 #    define GREENLET_USE_CFRAME 0
-#    define GREENLET_PY310 0
 #endif
 
 
-
 #if PY_VERSION_HEX >= 0x30B00A4
 /*
 Greenlet won't compile on anything older than Python 3.11 alpha 4 (see
@@ -124,4 +129,8 @@ static inline void PyThreadState_LeaveTracing(PyThreadState *tstate)
 }
 #endif
 
+#if !defined(Py_C_RECURSION_LIMIT) && defined(C_RECURSION_LIMIT)
+#  define Py_C_RECURSION_LIMIT C_RECURSION_LIMIT
+#endif
+
 #endif /* GREENLET_CPYTHON_COMPAT_H */
diff --git a/src/greenlet/greenlet_greenlet.hpp b/src/greenlet/greenlet_greenlet.hpp
index d52ce1fd..6da6841f 100644
--- a/src/greenlet/greenlet_greenlet.hpp
+++ b/src/greenlet/greenlet_greenlet.hpp
@@ -23,6 +23,7 @@ using greenlet::refs::BorrowedGreenlet;
 #endif
 
 #if GREENLET_PY312
+#  define Py_BUILD_CORE
 #  include "internal/pycore_frame.h"
 #endif