diff --git a/tsinfer/inference.py b/tsinfer/inference.py
index 94d13685..ce8dbc86 100644
--- a/tsinfer/inference.py
+++ b/tsinfer/inference.py
@@ -475,35 +475,50 @@ def insert_sites(self, tables):
         metadata = self.sample_data.sites_metadata[:]
         position = self.sample_data.sites_position[:]
         _, node, derived_state, parent = self.tree_sequence_builder.dump_mutations()
+        num_non_inference_sites = np.sum(inference == 0)
         logger.info(
             "Starting mutation positioning for {} non inference sites".format(
-                np.sum(inference == 0)))
+                num_non_inference_sites))
+
         progress_monitor = self.progress_monitor.get("ms_sites", num_sites)
-        inferred_site = 0
-        trees = ts.trees()
-        tree = next(trees)
-        for site_id, genotypes in self.sample_data.genotypes():
-            x = position[site_id]
-            while tree.interval[1] <= x:
-                tree = next(trees)
-            assert tree.interval[0] <= x < tree.interval[1]
-            tables.sites.add_row(
-                position=x,
-                ancestral_state=alleles[site_id][0],
-                metadata=self.encode_metadata(metadata[site_id]))
-            if inference[site_id] == 1:
+        if num_non_inference_sites > 0:
+            inferred_site = 0
+            trees = ts.trees()
+            tree = next(trees)
+            for site_id, genotypes in self.sample_data.genotypes():
+                x = position[site_id]
+                while tree.interval[1] <= x:
+                    tree = next(trees)
+                assert tree.interval[0] <= x < tree.interval[1]
+                tables.sites.add_row(
+                    position=x,
+                    ancestral_state=alleles[site_id][0],
+                    metadata=self.encode_metadata(metadata[site_id]))
+                if inference[site_id] == 1:
+                    tables.mutations.add_row(
+                        site=site_id, node=node[inferred_site],
+                        derived_state=alleles[site_id][derived_state[inferred_site]])
+                    inferred_site += 1
+                elif ts.num_edges > 0:
+                    self.locate_mutations_on_tree(
+                        tree, site_id, genotypes, alleles[site_id], tables.mutations)
+                else:
+                    # If we have no tree topology this is all we can do.
+                    self.locate_mutations_over_samples(
+                        site_id, genotypes, alleles[site_id], tables.mutations)
+                progress_monitor.update()
+        else:
+            # Simple case where all sites are inference sites.
+            for site_id in range(self.sample_data.num_sites):
+                x = position[site_id]
+                tables.sites.add_row(
+                    position=x,
+                    ancestral_state=alleles[site_id][0],
+                    metadata=self.encode_metadata(metadata[site_id]))
                 tables.mutations.add_row(
-                    site=site_id, node=node[inferred_site],
-                    derived_state=alleles[site_id][derived_state[inferred_site]])
-                inferred_site += 1
-            elif ts.num_edges > 0:
-                self.locate_mutations_on_tree(
-                    tree, site_id, genotypes, alleles[site_id], tables.mutations)
-            else:
-                # If we have no tree topology this is all we can do.
-                self.locate_mutations_over_samples(
-                    site_id, genotypes, alleles[site_id], tables.mutations)
-            progress_monitor.update()
+                    site=site_id, node=node[site_id],
+                    derived_state=alleles[site_id][derived_state[site_id]])
+                progress_monitor.update()
         progress_monitor.close()
 
     def get_samples_tree_sequence(self):