diff --git a/CHANGELOG.md b/CHANGELOG.md
index 6203d20..c1ff94e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,10 @@
 - A debug file is opened (created) lazily, in particular not at initialization if the initial log level is 0.
 - We give up on only splitting the flushing backend files at toplevel log boundaries: now a log open and log close can be in different files.
 
+### Fixed
+
+- Outdated README comment: local debug runtimes are not restricted to functions.
+
 ## [2.0.1] -- 2024-09-08
 
 ### Changed
diff --git a/README.md b/README.md
index 61a018f..fff37fe 100644
--- a/README.md
+++ b/README.md
@@ -1300,7 +1300,7 @@ For programs with threads or domains running concurrently, you need to ensure th
 
 We offer three helpers for dealing with multiple debug runtimes. There is an optional runtime instance-level setting `global_prefix`, which adds the given information to all log headers coming from the instance.
 
-There are extension points `%debug_l_sexp`, `%track_l_sexp`, etc. They call a function `_get_local_debug_runtime ()` and unpack the argument as `module Debug_runtime` (in a function body). The feature helps using a runtime instance dedicated to a thread or domain, since for example `_get_local_debug_runtime` can retrieve the runtime using `Domain.DLS`. To avoid surprises, this feature only takes effect for directly annotated functions, and unpacks a `Debug_runtime` inside the function body, so that we get the appropriate runtime for the dynamic local scope.
+There are extension points `%debug_l_sexp`, `%track_l_sexp`, etc. They call a function `_get_local_debug_runtime ()` and unpack the argument as `module Debug_runtime` (in a function body). The feature helps using a runtime instance dedicated to a thread or domain, since for example `_get_local_debug_runtime` can retrieve the runtime using `Domain.DLS`. To avoid surprises, in case of directly annotated functions, this feature unpacks a `Debug_runtime` inside the function body, so that we get the appropriate runtime for the dynamic local scope.
 
 NOTE: it's important to annotate functions that might be called from threads (spawned domains) using the `_l_` variants of extension points, e.g. `%debug_l_sexp` (not `%debug_sexp`!). For clearest output, should configure `_get_local_debug_runtime ()` to return the same runtime as the `Debug_runtime` module that is in a file-wide scope, when called from the main thread / main domain.
 
diff --git a/dune-project b/dune-project
index fe9b714..2f116e8 100644
--- a/dune-project
+++ b/dune-project
@@ -15,7 +15,7 @@
 
 (documentation https://lukstafi.github.io/ppx_minidebug/ppx_minidebug)
 
-(version 2.0.1)
+(version 2.0.2)
 
 (package
  (name ppx_minidebug)
diff --git a/index.mld b/index.mld
index a506382..5f348a1 100644
--- a/index.mld
+++ b/index.mld
@@ -1370,7 +1370,7 @@ For programs with threads or domains running concurrently, you need to ensure th
 
 We offer three helpers for dealing with multiple debug runtimes. There is an optional runtime instance-level setting [global_prefix], which adds the given information to all log headers coming from the instance.
 
-There are extension points [%debug_l_sexp], [%track_l_sexp], etc. They call a function [_get_local_debug_runtime ()] and unpack the argument as [module Debug_runtime] (in a function body). The feature helps using a runtime instance dedicated to a thread or domain, since for example [_get_local_debug_runtime] can retrieve the runtime using [Domain.DLS]. To avoid surprises, this feature only takes effect for directly annotated functions, and unpacks a [Debug_runtime] inside the function body, so that we get the appropriate runtime for the dynamic local scope.
+There are extension points [%debug_l_sexp], [%track_l_sexp], etc. They call a function [_get_local_debug_runtime ()] and unpack the argument as [module Debug_runtime] (in a function body). The feature helps using a runtime instance dedicated to a thread or domain, since for example [_get_local_debug_runtime] can retrieve the runtime using [Domain.DLS]. To avoid surprises, in case of directly annotated functions, this feature unpacks a [Debug_runtime] inside the function body, so that we get the appropriate runtime for the dynamic local scope.
 
 NOTE: it's important to annotate functions that might be called from threads (spawned domains) using the [_l_] variants of extension points, e.g. [%debug_l_sexp] (not [%debug_sexp]!). For clearest output, should configure [_get_local_debug_runtime ()] to return the same runtime as the [Debug_runtime] module that is in a file-wide scope, when called from the main thread / main domain.
 
diff --git a/minidebug_runtime.mli b/minidebug_runtime.mli
index e847d39..c0c3527 100644
--- a/minidebug_runtime.mli
+++ b/minidebug_runtime.mli
@@ -81,8 +81,10 @@ val shared_config :
     instead of a file name, will use [global_prefix] instead for the anchor links. The
     setting [toc_entry] controls the selection of headers to include in a ToC (it defaults
     to [And []], which means including all entries).
-    
-    [log_level], is provided, specifies {!Shared_config.init_log_level}.  *)
+
+    [log_level], by default 9, specifies {!Shared_config.init_log_level}. This is the
+    initial log level. In particular, the header "BEGIN DEBUG SESSION" is only printed if
+    (initial) [log_level > 0]. *)
 
 (** When using the
     {{:http://lukstafi.github.io/ppx_minidebug/ppx_minidebug/Minidebug_runtime/index.html}
diff --git a/ppx_minidebug.opam b/ppx_minidebug.opam
index b93ebe5..acb088d 100644
--- a/ppx_minidebug.opam
+++ b/ppx_minidebug.opam
@@ -1,6 +1,6 @@
 # This file is generated by dune, edit dune-project instead
 opam-version: "2.0"
-version: "2.0.1"
+version: "2.0.2"
 synopsis: "Debug logs for selected functions and let-bindings"
 description:
   "Formatted logs of let-bound values, function arguments and results; `if` and `match` branches taken. Optionally, as collapsible HTML trees with highlights."