diff --git a/cmdstanpy/stanfit/mcmc.py b/cmdstanpy/stanfit/mcmc.py
index 16c4e09c..d1fa0fe0 100644
--- a/cmdstanpy/stanfit/mcmc.py
+++ b/cmdstanpy/stanfit/mcmc.py
@@ -448,11 +448,11 @@ def summary(
     ) -> pd.DataFrame:
         """
         Run cmdstan/bin/stansummary over all output CSV files, assemble
-        summary into DataFrame object; first row contains summary statistics
-        for total joint log probability `lp__`, remaining rows contain summary
+        summary into DataFrame object.  The first row contains statistics
+        for the total joint log probability `lp__`, but is omitted when the
+        Stan model has no parameters.  The remaining rows contain summary
         statistics for all parameters, transformed parameters, and generated
-        quantities variables listed in the order in which they were declared
-        in the Stan program.
+        quantities variables, in program declaration order.
 
         :param percentiles: Ordered non-empty sequence of percentiles to report.
             Must be integers from (1, 99), inclusive. Defaults to
@@ -467,7 +467,6 @@ def summary(
 
         :return: pandas.DataFrame
         """
-
         if len(percentiles) == 0:
             raise ValueError(
                 'Invalid percentiles argument, must be ordered'
@@ -526,7 +525,14 @@ def summary(
                 comment='#',
                 float_precision='high',
             )
-        mask = [x == 'lp__' or not x.endswith('__') for x in summary_data.index]
+        mask = (
+            [not x.endswith('__') for x in summary_data.index]
+            if self._is_fixed_param
+            else [
+                x == 'lp__' or not x.endswith('__') for x in summary_data.index
+            ]
+        )
+        summary_data.index.name = None
         return summary_data[mask]
 
     def diagnose(self) -> Optional[str]:
diff --git a/test/test_sample.py b/test/test_sample.py
index 1bb26184..6a01515d 100644
--- a/test/test_sample.py
+++ b/test/test_sample.py
@@ -598,6 +598,8 @@ def test_fixed_param_unspecified(self):
             iter_sampling=100, show_progress=False
         )
         self.assertEqual(datagen_fit.step_size, None)
+        summary = datagen_fit.summary()
+        self.assertNotIn('lp__', list(summary.index))
 
         exe_only = os.path.join(DATAFILES_PATH, 'exe_only')
         shutil.copyfile(datagen_model.exe_file, exe_only)
@@ -608,6 +610,8 @@ def test_fixed_param_unspecified(self):
         )
         self.assertEqual(datagen2_fit.chains, 4)
         self.assertEqual(datagen2_fit.step_size, None)
+        summary = datagen2_fit.summary()
+        self.assertNotIn('lp__', list(summary.index))
 
     def test_bernoulli_file_with_space(self):
         self.test_bernoulli_good('bernoulli with space in name.stan')
@@ -743,11 +747,11 @@ def test_validate_good_run(self):
 
         self.assertEqual(
             list(fit.draws_pd(vars=['theta', 'lp__']).columns),
-            ['theta', 'lp__']
+            ['theta', 'lp__'],
         )
         self.assertEqual(
             list(fit.draws_pd(vars=['lp__', 'theta']).columns),
-            ['lp__', 'theta']
+            ['lp__', 'theta'],
         )
 
         summary = fit.summary()
@@ -756,6 +760,9 @@ def test_validate_good_run(self):
         self.assertIn('95%', list(summary.columns))
         self.assertNotIn('1%', list(summary.columns))
         self.assertNotIn('99%', list(summary.columns))
+        self.assertEqual(summary.index.name, None)
+        self.assertIn('lp__', list(summary.index))
+        self.assertIn('theta', list(summary.index))
 
         summary = fit.summary(percentiles=[1, 45, 99])
         self.assertIn('1%', list(summary.columns))