#5840: dont claim we dont support TLS.
diff --git a/Doc/c-api/init.rst b/Doc/c-api/init.rst
index 281432b..4fb428d 100644
--- a/Doc/c-api/init.rst
+++ b/Doc/c-api/init.rst
@@ -419,10 +419,9 @@
The Python interpreter needs to keep some bookkeeping information separate per
thread --- for this it uses a data structure called :ctype:`PyThreadState`.
There's one global variable, however: the pointer to the current
-:ctype:`PyThreadState` structure. While most thread packages have a way to
-store "per-thread global data," Python's internal platform independent thread
-abstraction doesn't support this yet. Therefore, the current thread state must
-be manipulated explicitly.
+:ctype:`PyThreadState` structure. Before the addition of :dfn:`thread-local
+storage` (:dfn:`TLS`) the current thread state had to be manipulated
+explicitly.
This is easy enough in most cases. Most code manipulating the global
interpreter lock has the following simple structure::