diff --git a/egs/librispeech/ASR/pruned_transducer_stateless/decode.py b/egs/librispeech/ASR/pruned_transducer_stateless/decode.py
index 8e924bf96c..49b1308b0f 100755
--- a/egs/librispeech/ASR/pruned_transducer_stateless/decode.py
+++ b/egs/librispeech/ASR/pruned_transducer_stateless/decode.py
@@ -98,27 +98,28 @@ def get_parser():
         "--epoch",
         type=int,
         default=28,
-        help="It specifies the checkpoint to use for decoding."
-        "Note: Epoch counts from 0.",
+        help="""It specifies the checkpoint to use for decoding.
+        Note: Epoch counts from 0.
+        You can specify --avg to use more checkpoints for model averaging.""",
     )
+
     parser.add_argument(
-        "--avg",
+        "--iter",
         type=int,
-        default=15,
-        help="Number of checkpoints to average. Automatically select "
-        "consecutive checkpoints before the checkpoint specified by "
-        "'--epoch'. ",
+        default=0,
+        help="""If positive, --epoch is ignored and it
+        will use the checkpoint exp_dir/checkpoint-iter.pt.
+        You can specify --avg to use more checkpoints for model averaging.
+        """,
     )
 
     parser.add_argument(
-        "--avg-last-n",
+        "--avg",
         type=int,
-        default=0,
-        help="""If positive, --epoch and --avg are ignored and it
-        will use the last n checkpoints exp_dir/checkpoint-xxx.pt
-        where xxx is the number of processed batches while
-        saving that checkpoint.
-        """,
+        default=15,
+        help="Number of checkpoints to average. Automatically select "
+        "consecutive checkpoints before the checkpoint specified by "
+        "'--epoch' and '--iter'",
     )
 
     parser.add_argument(
@@ -453,13 +454,19 @@ def main():
     )
     params.res_dir = params.exp_dir / params.decoding_method
 
-    params.suffix = f"epoch-{params.epoch}-avg-{params.avg}"
+    if params.iter > 0:
+        params.suffix = f"iter-{params.iter}-avg-{params.avg}"
+    else:
+        params.suffix = f"epoch-{params.epoch}-avg-{params.avg}"
+
     if "fast_beam_search" in params.decoding_method:
         params.suffix += f"-beam-{params.beam}"
         params.suffix += f"-max-contexts-{params.max_contexts}"
         params.suffix += f"-max-states-{params.max_states}"
     elif "beam_search" in params.decoding_method:
-        params.suffix += f"-beam-{params.beam_size}"
+        params.suffix += (
+            f"-{params.decoding_method}-beam-size-{params.beam_size}"
+        )
     else:
         params.suffix += f"-context-{params.context_size}"
         params.suffix += f"-max-sym-per-frame-{params.max_sym_per_frame}"
@@ -485,8 +492,20 @@ def main():
     logging.info("About to create model")
     model = get_transducer_model(params)
 
-    if params.avg_last_n > 0:
-        filenames = find_checkpoints(params.exp_dir)[: params.avg_last_n]
+    if params.iter > 0:
+        filenames = find_checkpoints(params.exp_dir, iteration=-params.iter)[
+            : params.avg
+        ]
+        if len(filenames) == 0:
+            raise ValueError(
+                f"No checkpoints found for"
+                f" --iter {params.iter}, --avg {params.avg}"
+            )
+        elif len(filenames) < params.avg:
+            raise ValueError(
+                f"Not enough checkpoints ({len(filenames)}) found for"
+                f" --iter {params.iter}, --avg {params.avg}"
+            )
         logging.info(f"averaging {filenames}")
         model.to(device)
         model.load_state_dict(average_checkpoints(filenames, device=device))
diff --git a/icefall/checkpoint.py b/icefall/checkpoint.py
index 251456c955..1ef05d964a 100644
--- a/icefall/checkpoint.py
+++ b/icefall/checkpoint.py
@@ -216,27 +216,62 @@ def save_checkpoint_with_global_batch_idx(
     )
 
 
-def find_checkpoints(out_dir: Path) -> List[str]:
+def find_checkpoints(out_dir: Path, iteration: int = 0) -> List[str]:
     """Find all available checkpoints in a directory.
 
     The checkpoint filenames have the form: `checkpoint-xxx.pt`
     where xxx is a numerical value.
 
+    Assume you have the following checkpoints in the folder `foo`:
+
+        - checkpoint-1.pt
+        - checkpoint-20.pt
+        - checkpoint-300.pt
+        - checkpoint-4000.pt
+
+    Case 1 (Return all checkpoints)::
+
+      find_checkpoints(out_dir='foo')
+
+    Case 2 (Return checkpoints newer than checkpoint-20.pt, i.e.,
+    checkpoint-4000.pt, checkpoint-300.pt, and checkpoint-20.pt)
+
+        find_checkpoints(out_dir='foo', iteration=20)
+
+    Case 3 (Return checkpoints older than checkpoint-20.pt, i.e.,
+    checkpoint-20.pt, checkpoint-1.pt)::
+
+        find_checkpoints(out_dir='foo', iteration=-20)
+
     Args:
       out_dir:
         The directory where to search for checkpoints.
+      iteration:
+        If it is 0, return all available checkpoints.
+        If it is positive, return the checkpoints whose iteration number is
+        greater than or equal to `iteration`.
+        If it is negative, return the checkpoints whose iteration number is
+        less than or equal to `-iteration`.
     Returns:
       Return a list of checkpoint filenames, sorted in descending
       order by the numerical value in the filename.
     """
     checkpoints = list(glob.glob(f"{out_dir}/checkpoint-[0-9]*.pt"))
     pattern = re.compile(r"checkpoint-([0-9]+).pt")
-    idx_checkpoints = [
+    iter_checkpoints = [
         (int(pattern.search(c).group(1)), c) for c in checkpoints
     ]
+    # iter_checkpoints is a list of tuples. Each tuple contains
+    # two elements: (iteration_number, checkpoint-iteration_number.pt)
+
+    iter_checkpoints = sorted(
+        iter_checkpoints, reverse=True, key=lambda x: x[0]
+    )
+    if iteration >= 0:
+        ans = [ic[1] for ic in iter_checkpoints if ic[0] >= iteration]
+    else:
+        ans = [ic[1] for ic in iter_checkpoints if ic[0] <= -iteration]
 
-    idx_checkpoints = sorted(idx_checkpoints, reverse=True, key=lambda x: x[0])
-    ans = [ic[1] for ic in idx_checkpoints]
     return ans