diff --git a/Lib/test/test_asyncgen.py b/Lib/test/test_asyncgen.py
index 24b20bec2b2..fb6321d2264 100644
--- a/Lib/test/test_asyncgen.py
+++ b/Lib/test/test_asyncgen.py
@@ -1128,7 +1128,7 @@ async def main():
 
         self.assertEqual([], messages)
 
-    def test_async_gen_await_anext_twice(self):
+    def test_async_gen_await_same_anext_coro_twice(self):
         async def async_iterate():
             yield 1
             yield 2
@@ -1147,7 +1147,7 @@ async def run():
 
         self.loop.run_until_complete(run())
 
-    def test_async_gen_await_aclose_twice(self):
+    def test_async_gen_await_same_aclose_coro_twice(self):
         async def async_iterate():
             yield 1
             yield 2
@@ -1164,6 +1164,32 @@ async def run():
 
         self.loop.run_until_complete(run())
 
+    def test_async_gen_aclose_twice_with_different_coros(self):
+        # Regression test for https://bugs.python.org/issue39606
+        async def async_iterate():
+            yield 1
+            yield 2
+
+        async def run():
+            it = async_iterate()
+            await it.aclose()
+            await it.aclose()
+
+        self.loop.run_until_complete(run())
+
+    def test_async_gen_aclose_after_exhaustion(self):
+        # Regression test for https://bugs.python.org/issue39606
+        async def async_iterate():
+            yield 1
+            yield 2
+
+        async def run():
+            it = async_iterate()
+            async for _ in it:
+                pass
+            await it.aclose()
+
+        self.loop.run_until_complete(run())
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/Misc/NEWS.d/next/Core and Builtins/2020-02-11-23-59-07.bpo-39606.a72Sxc.rst b/Misc/NEWS.d/next/Core and Builtins/2020-02-11-23-59-07.bpo-39606.a72Sxc.rst
new file mode 100644
index 00000000000..b7cbe4e91f5
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2020-02-11-23-59-07.bpo-39606.a72Sxc.rst	
@@ -0,0 +1,2 @@
+Fix regression caused by fix for bpo-39386, that prevented calling
+``aclose`` on an async generator that had already been closed or exhausted.
diff --git a/Objects/genobject.c b/Objects/genobject.c
index 576d6856c7f..0efd57de7a5 100644
--- a/Objects/genobject.c
+++ b/Objects/genobject.c
@@ -1797,16 +1797,22 @@ async_gen_athrow_send(PyAsyncGenAThrow *o, PyObject *arg)
     PyFrameObject *f = gen->gi_frame;
     PyObject *retval;
 
-    if (f == NULL || f->f_stacktop == NULL ||
-            o->agt_state == AWAITABLE_STATE_CLOSED) {
+    if (o->agt_state == AWAITABLE_STATE_CLOSED) {
         PyErr_SetString(
             PyExc_RuntimeError,
             "cannot reuse already awaited aclose()/athrow()");
         return NULL;
     }
 
+    if (f == NULL || f->f_stacktop == NULL) {
+        o->agt_state = AWAITABLE_STATE_CLOSED;
+        PyErr_SetNone(PyExc_StopIteration);
+        return NULL;
+    }
+
     if (o->agt_state == AWAITABLE_STATE_INIT) {
         if (o->agt_gen->ag_running_async) {
+            o->agt_state = AWAITABLE_STATE_CLOSED;
             if (o->agt_args == NULL) {
                 PyErr_SetString(
                     PyExc_RuntimeError,
@@ -1878,7 +1884,6 @@ async_gen_athrow_send(PyAsyncGenAThrow *o, PyObject *arg)
         /* aclose() mode */
         if (retval) {
             if (_PyAsyncGenWrappedValue_CheckExact(retval)) {
-                o->agt_gen->ag_running_async = 0;
                 Py_DECREF(retval);
                 goto yield_close;
             }
@@ -1893,16 +1898,17 @@ async_gen_athrow_send(PyAsyncGenAThrow *o, PyObject *arg)
 
 yield_close:
     o->agt_gen->ag_running_async = 0;
+    o->agt_state = AWAITABLE_STATE_CLOSED;
     PyErr_SetString(
         PyExc_RuntimeError, ASYNC_GEN_IGNORED_EXIT_MSG);
     return NULL;
 
 check_error:
     o->agt_gen->ag_running_async = 0;
+    o->agt_state = AWAITABLE_STATE_CLOSED;
     if (PyErr_ExceptionMatches(PyExc_StopAsyncIteration) ||
             PyErr_ExceptionMatches(PyExc_GeneratorExit))
     {
-        o->agt_state = AWAITABLE_STATE_CLOSED;
         if (o->agt_args == NULL) {
             /* when aclose() is called we don't want to propagate
                StopAsyncIteration or GeneratorExit; just raise
@@ -1936,6 +1942,7 @@ async_gen_athrow_throw(PyAsyncGenAThrow *o, PyObject *args)
         /* aclose() mode */
         if (retval && _PyAsyncGenWrappedValue_CheckExact(retval)) {
             o->agt_gen->ag_running_async = 0;
+            o->agt_state = AWAITABLE_STATE_CLOSED;
             Py_DECREF(retval);
             PyErr_SetString(PyExc_RuntimeError, ASYNC_GEN_IGNORED_EXIT_MSG);
             return NULL;