diff --git a/pchealthstream2py/pchealth.py b/pchealthstream2py/pchealth.py
index cd223e4..e96ab55 100644
--- a/pchealthstream2py/pchealth.py
+++ b/pchealthstream2py/pchealth.py
@@ -252,7 +252,7 @@ def __init__(
         # `join()` with "TypeError: 'Event' object is not callable".
         self._stop_event: threading.Event = threading.Event()
         # The thread currently running `run`, or None while the reader has never
-        # been opened. It is `self` for the first run (see `_start_worker`).
+        # been opened (see `_start_worker`).
         self._worker: Optional[threading.Thread] = None
 
     def open(self):
@@ -295,21 +295,40 @@ def _stop_previous_worker(self):
             )
 
     def _start_worker(self):
-        """Run `run` in a daemon thread, reusing `self` for the very first run.
+        """Run `run` in a fresh daemon thread: one per `open()`.
 
-        A `threading.Thread` can only be started once, so from the second
-        `open()` on the work has to go in a fresh thread. The first `open()`
-        still starts `self`, which keeps `is_alive()`, `join()` and the rest of
-        the inherited `Thread` API behaving exactly as they always have.
+        A `threading.Thread` can only be started once, so a reusable reader
+        can't run its work in `self` -- not even the first time, or `self` would
+        be a finished thread standing in for the reader from the second `open()`
+        on. `is_alive()` and `join()` are overridden to follow the current
+        worker, so they keep meaning "is it reading" and "wait for it to stop".
         """
-        if self._worker is None:
-            self._worker = self
-            self.start()
-        else:
-            self._worker = threading.Thread(
-                target=self.run, daemon=True, name=f"{self.name}-worker"
-            )
-            self._worker.start()
+        self._worker = threading.Thread(
+            target=self.run, daemon=True, name=f"{self.name}-worker"
+        )
+        self._worker.start()
+
+    def _current_worker_is_another_thread(self) -> bool:
+        worker = self._worker
+        return worker is not None and worker is not self
+
+    def is_alive(self) -> bool:
+        """Whether the reader is currently reading, whichever thread is doing it.
+
+        The work runs in a per-`open()` worker thread (see `_start_worker`), not
+        in `self`, so the inherited `Thread.is_alive` would describe the wrong
+        thread. (A reader started the legacy way, with `start()` rather than
+        `open()`, has no worker and answers for `self` as before.)
+        """
+        if self._current_worker_is_another_thread():
+            return self._worker.is_alive()
+        return super().is_alive()
+
+    def join(self, timeout: Optional[float] = None) -> None:
+        """Wait for the current run's worker thread to finish (see `is_alive`)."""
+        if self._current_worker_is_another_thread():
+            return self._worker.join(timeout)
+        return super().join(timeout)
 
     def read(self):
         """Returns one data item
diff --git a/pchealthstream2py/tests/simple_test.py b/pchealthstream2py/tests/simple_test.py
index 19ebec8..59ea77b 100644
--- a/pchealthstream2py/tests/simple_test.py
+++ b/pchealthstream2py/tests/simple_test.py
@@ -103,3 +103,27 @@ def test_reopen_does_not_leak_worker_threads():
     for worker in workers:
         worker.join(timeout=10)
         assert not worker.is_alive()
+
+
+def test_thread_api_follows_the_current_worker_after_reopen():
+    """`is_alive()` / `join()` must describe the run in progress, not the first one.
+
+    #3 ran the first `open()` in `self` and later ones in fresh threads, so after
+    a reopen the inherited `Thread.is_alive` answered False for a reader that was
+    busy reading (it described the finished first-run thread), and `join()`
+    returned at once instead of waiting for the worker to stop.
+    """
+    reader = StatusInfoReader(read_interval_ms=50)
+    with reader:
+        time.sleep(0.1)
+    reader.join(timeout=10)
+
+    reader.open()
+    try:
+        time.sleep(0.1)
+        assert reader.is_alive()
+    finally:
+        reader.close()
+    reader.join(timeout=10)
+    assert not reader.is_alive()
+    assert not reader._worker.is_alive()