diff --git a/src/uproot/interpretation/objects.py b/src/uproot/interpretation/objects.py
index 891d26735..0a01f30d9 100644
--- a/src/uproot/interpretation/objects.py
+++ b/src/uproot/interpretation/objects.py
@@ -596,15 +596,16 @@ class AsStridedObjects(uproot.interpretation.numerical.AsDtype):
 
     def __init__(self, model, members, original=None):
         all_headers_prepended = False
-        first_value_loc = 0
-        while members[first_value_loc] == (None, None):
-            first_value_loc += 1
+
+        for first_value_loc in range(len(members)):
+            if members[first_value_loc] != (None, None):
+                break
 
         for i in range(first_value_loc, len(members)):
             member, value = members[i]
             if member is not None and not all_headers_prepended:
                 all_headers_prepended = True
-            if member is None and all_headers_prepended:
+            if member is None and all_headers_prepended or len(members) == 1:
                 all_headers_prepended = False
                 del members[i]
 
diff --git a/tests/test_0910-fix_906_members_non_numerical_branches.py b/tests/test_0910-fix_906_members_non_numerical_branches.py
new file mode 100644
index 000000000..ed03c7de5
--- /dev/null
+++ b/tests/test_0910-fix_906_members_non_numerical_branches.py
@@ -0,0 +1,14 @@
+import uproot
+
+from skhep_testdata import data_path
+
+
+def test_fix_906_members_non_numerical_branches():
+    filename = data_path("uproot-issue-798.root")  # PHYSLITE example file
+    f = uproot.open(filename)
+    tree = f["CollectionTree"]
+
+    assert (
+        str(tree["EventInfo"].interpretation)
+        == "AsStridedObjects(Model_xAOD_3a3a_EventInfo_5f_v1_v1)"
+    )