diff --git a/coverage/control.py b/coverage/control.py
index ca757e9e1..c4e325212 100644
--- a/coverage/control.py
+++ b/coverage/control.py
@@ -536,7 +536,7 @@ def _init_for_start(self) -> None:
 
         self._core = Core(
             warn=self._warn,
-            timid=self.config.timid,
+            config=self.config,
             metacov=self._metacov,
         )
         self._collector = Collector(
diff --git a/coverage/core.py b/coverage/core.py
index b8916b683..7affeb2e2 100644
--- a/coverage/core.py
+++ b/coverage/core.py
@@ -10,6 +10,7 @@
 from typing import Any
 
 from coverage import env
+from coverage.config import CoverageConfig
 from coverage.disposition import FileDisposition
 from coverage.exceptions import ConfigError
 from coverage.pytracer import PyTracer
@@ -49,16 +50,9 @@ class Core:
     packed_arcs: bool
     systrace: bool
 
-    def __init__(self,
-        warn: TWarnFn,
-        timid: bool,
-        metacov: bool,
-    ) -> None:
-        # Defaults
-        self.tracer_kwargs = {}
-
+    def __init__(self, warn: TWarnFn, config: CoverageConfig, metacov: bool) -> None:
         core_name: str | None
-        if timid:
+        if config.timid:
             core_name = "pytrace"
         else:
             core_name = os.getenv("COVERAGE_CORE")
@@ -76,9 +70,11 @@ def __init__(self,
                 else:
                     core_name = "pytrace"
 
+        self.tracer_kwargs = {}
+
         if core_name == "sysmon":
             self.tracer_class = SysMonitor
-            self.tracer_kwargs = {"tool_id": 3 if metacov else 1}
+            self.tracer_kwargs["tool_id"] = 3 if metacov else 1
             self.file_disposition_class = FileDisposition
             self.supports_plugins = False
             self.packed_arcs = False
diff --git a/coverage/env.py b/coverage/env.py
index 3bae7e51a..792ed1d5f 100644
--- a/coverage/env.py
+++ b/coverage/env.py
@@ -112,6 +112,12 @@ class PYBEHAVIOR:
     # https://github.com/python/cpython/issues/113728
     lasti_is_yield = (PYVERSION[:2] != (3, 13))
 
+    # Does sys.monitoring support BRANCH_TAKEN?
+    branch_taken = (
+        pep669 and
+        hasattr(sys.monitoring.events, "BRANCH_TAKEN") # type:ignore[attr-defined]
+    )
+
 
 # Coverage.py specifics, about testing scenarios. See tests/testenv.py also.
 
diff --git a/coverage/sysmon.py b/coverage/sysmon.py
index ef54292f3..bbbe42390 100644
--- a/coverage/sysmon.py
+++ b/coverage/sysmon.py
@@ -23,6 +23,7 @@
     cast,
 )
 
+from coverage import env
 from coverage.debug import short_filename, short_stack
 from coverage.types import (
     AnyCallable,
@@ -352,8 +353,9 @@ def sysmon_py_start(self, code: CodeType, instruction_offset: int) -> MonitorRet
                             #
                             | events.PY_RESUME
                             # | events.PY_YIELD
-                            | events.LINE,
-                            # | events.BRANCH
+                            | events.LINE
+                            | events.BRANCH_TAKEN
+                            | events.BRANCH_NOT_TAKEN
                             # | events.JUMP
                         )
                         self.local_event_codes[id(code)] = code