diff --git a/esphome/espota2.py b/esphome/espota2.py
index 09b83cee0c3..3e7b5540855 100644
--- a/esphome/espota2.py
+++ b/esphome/espota2.py
@@ -479,12 +479,14 @@ class NoiseSocketWrapper:
             raise OTAError(f"Device rejected the noise handshake: {reason}")
         try:
             self._handshake.read_message(payload[1:])
-        except (ValueError, self._invalid_tag) as err:
-            # InvalidTag is a wrong key; ValueError covers a device sending an
-            # invalid curve point, which cryptography rejects during the DH
+        except self._invalid_tag as err:
             raise OTAKeyRejected(
                 "Noise handshake failed; is the OTA encryption key correct?"
             ) from err
+        except ValueError as err:
+            # An invalid curve point, rejected by cryptography during the DH;
+            # the device is broken, not the key
+            raise OTAError(f"Noise handshake failed: {err}") from err
         self._encrypt, self._decrypt = self._handshake.get_ciphers()
 
     def sendall(self, data: bytes) -> None:
diff --git a/tests/unit_tests/test_espota2_noise.py b/tests/unit_tests/test_espota2_noise.py
index 054dc7e86c8..f674032437a 100644
--- a/tests/unit_tests/test_espota2_noise.py
+++ b/tests/unit_tests/test_espota2_noise.py
@@ -550,21 +550,21 @@ def test_handshake_reject_with_other_reason() -> None:
 
 
 def test_handshake_garbage_second_message() -> None:
-    """A valid-looking point with a garbage MAC fails cleanly."""
+    """A valid-looking point with a garbage MAC is a key failure."""
     wrapper = _wrapper(_frame(b"\x00" + bytes(range(48))))
     with pytest.raises(
-        espota2.OTAError, match="handshake failed; is the OTA encryption key"
+        espota2.OTAKeyRejected, match="handshake failed; is the OTA encryption key"
     ):
         wrapper.do_handshake()
 
 
 def test_handshake_invalid_curve_point() -> None:
-    """An all-zero x25519 point is rejected as a clean error, not a crash."""
+    """An all-zero x25519 point is a clean error, not a crash, and not a
+    key failure: it must not spend the old_key retry."""
     wrapper = _wrapper(_frame(b"\x00" + bytes(48)))
-    with pytest.raises(
-        espota2.OTAError, match="handshake failed; is the OTA encryption key"
-    ):
+    with pytest.raises(espota2.OTAError, match="handshake failed: ") as info:
         wrapper.do_handshake()
+    assert not isinstance(info.value, espota2.OTAKeyRejected)
 
 
 def test_recv_closed_at_frame_boundary_returns_empty() -> None: