diff --git a/qiskit/pulse/instructions/delay.py b/qiskit/pulse/instructions/delay.py
index edaa406f4fcb..1b911c350731 100644
--- a/qiskit/pulse/instructions/delay.py
+++ b/qiskit/pulse/instructions/delay.py
@@ -47,10 +47,7 @@ def __init__(
         Args:
             duration: Length of time of the delay in terms of dt.
             channel: The channel that will have the delay.
-            name: Name of the delay for display purposes.
-
-        Raises:
-            PulseError: If `channel` cannot be delayed because it is a classical IO channel.
+            name: Name of the delay for display purposes.k
         """
         super().__init__(operands=(duration, channel), name=name)
 
diff --git a/qiskit/pulse/instructions/frequency.py b/qiskit/pulse/instructions/frequency.py
index dfff24ce9b48..15866e0ae79a 100644
--- a/qiskit/pulse/instructions/frequency.py
+++ b/qiskit/pulse/instructions/frequency.py
@@ -106,7 +106,7 @@ def __init__(
             frequency = float(frequency)
         if not isinstance(channel, PulseChannel):
             raise PulseError(
-                "The `channel` argument to `SetFrequency` must be of type `channels.PulseChannel`."
+                "The `channel` argument to `ShiftFrequency` must be of type `channels.PulseChannel`."
             )
         super().__init__(operands=(frequency, channel), name=name)
 
diff --git a/test/python/pulse/test_transforms.py b/test/python/pulse/test_transforms.py
index 1cfb28f55245..e19d024c2b4f 100644
--- a/test/python/pulse/test_transforms.py
+++ b/test/python/pulse/test_transforms.py
@@ -364,7 +364,13 @@ def test_pad_no_delay_on_classical_io_channels(self):
             + Delay(delay, SnapshotChannel())
         )
 
-        self.assertEqual(transforms.pad(sched, until=15), sched)
+        ref_sched = (
+            Delay(delay, MemorySlot(0)).shift(20)
+            + Delay(delay, RegisterSlot(0)).shift(10)
+            + Delay(delay, SnapshotChannel())
+        )
+
+        self.assertEqual(transforms.pad(sched, until=15), ref_sched)
 
 
 def get_pulse_ids(schedules: List[Schedule]) -> Set[int]: