diff --git a/cmdstanpy/stanfit/mcmc.py b/cmdstanpy/stanfit/mcmc.py
index 53fb4de1..4d908033 100644
--- a/cmdstanpy/stanfit/mcmc.py
+++ b/cmdstanpy/stanfit/mcmc.py
@@ -441,6 +441,12 @@ def _assemble_draws(self) -> None:
                                 self._metric[chain, i, :] = [
                                     float(x) for x in xs
                                 ]
+                    else:  # unit_e changed in 2.34 to have an extra line
+                        pos = fd.tell()
+                        line = fd.readline().strip()
+                        if not line.startswith('#'):
+                            fd.seek(pos)
+
                 # process draws
                 for i in range(sampling_iter_start, num_draws):
                     line = fd.readline().strip()
diff --git a/cmdstanpy/utils/stancsv.py b/cmdstanpy/utils/stancsv.py
index d08181d2..1481cb5d 100644
--- a/cmdstanpy/utils/stancsv.py
+++ b/cmdstanpy/utils/stancsv.py
@@ -289,10 +289,16 @@ def scan_hmc_params(
         raise ValueError(
             'line {}: invalid step size: {}'.format(lineno, step_size)
         ) from e
-    if metric == 'unit_e':
-        return lineno
+    before_metric = fd.tell()
     line = fd.readline().strip()
     lineno += 1
+    if metric == 'unit_e':
+        if line.startswith("# No free parameters"):
+            return lineno
+        else:
+            fd.seek(before_metric)
+            return lineno - 1
+
     if not (
         (
             metric == 'diag_e'